Higgs won the prize with Belgium's Francois Englert. The Royal Swedish Academy of Sciences cited the two scientists for the "theoretical discovery of a mechanism that contributes to our understanding of the origin of mass of subatomic particles".
Their theories were confirmed last year by the discovery of the so-called Higgs particle at a laboratory in Geneva, the Royal Swedish Academy of Sciences said.
The academy decides the winners in a majority vote on the day of the announcement.
Professor Higgs, emeritus professor of theoretical physics at Edinburgh University, said: "I am overwhelmed to receive this award and thank the Royal Swedish Academy. I would also like to congratulate all those who have contributed to the discovery of this new particle and to thank my family, friends and colleagues for their support. I hope this recognition of fundamental science will help raise awareness of the value of blue-sky research."
Prof Higgs, a retired Edinburgh University professor, and Prof Englert theorised about the existence of the particle in the 1960s to provide an answer to a riddle: why matter has mass. The tiny particle, they believed, acts like molasses on snow - causing other basic building blocks of nature to stick together, slow down and form atoms.
But decades would pass before scientists at CERN, the Geneva-based European Organisation for Nuclear Research, were able to confirm its existence. The European particle physics laboratory announced the news in July of last year.
The collider cost 10 billion dollars (£6.2 billion) to build and run in a 17-mile (27-kilometre) tunnel beneath the Swiss-French border.
Only about one collision per trillion will produce one of the Higgs bosons in the collider, and it took CERN some time after the discovery of a new "Higgs-like" boson to decide that the particle was, in fact, very much like the Higgs boson expected in the original formulation, rather than a kind of variant.
The Higgs boson enables other fundamental particles to acquire their mass. Its discovery represents a major step in our understanding of the physical universe.
Professor Sir Timothy O'Shea, principal at the University of Edinburgh, said: "We are delighted at the news of this Nobel Prize award and congratulate Professor Peter Higgs on his achievement. The discovery of the Higgs particle will underpin the next generation of physics research, and this accolade is worthy recognition of its significance. Professor Higgs' work will continue to inspire scientists at Edinburgh and beyond."
Sir John Arbuthnott, president of the Royal Society of Edinburgh, Scotland's National Academy, said: "Peter Higgs is one of the great modern scientific minds.
"I am delighted Peter has been awarded a Nobel Prize for physics. This well-deserved honour is the ultimate recognition of the extraordinary contribution he has made to the understanding of the fundamental nature of matter".
"Peter maintains the Scottish tradition of inspired excellence in science and follows in the footsteps of outstanding RSE Fellows like James Clerk Maxwell and Lord Kelvin, whose work profoundly affect our lives today.
"Given the intense world wide competition for the brightest minds and the link between that and future wealth creation, the ability of Scotland to continue to attract and retain the finest minds is now even more important."
"The Fellows of the Royal Society of Edinburgh extend their heartfelt congratulations to one of our own, who has rightly received the highest of scientific accolades."
In March, Professor Higgs was given the Edinburgh Medal at a ceremony in the Scottish capital to recognise his significant contributions to the field of science and technology. Previous recipients have included three Nobel Prize winners.
He was also made a Companion of Honour in the New Year Honours list and the Higgs Prize was set up by the Scottish Government to recognise school pupils who excel in physics.
Other researchers, including Professor Englert, were also working separately on the same idea as Professor Higgs and published papers around the same time.
The Higgs boson explains why other elementary particles, the basic building blocks of the Universe, have mass.
Cern director-general Rolf Heuer congratulated the pair.
He said: "I'm thrilled that this year's Nobel Prize has gone to particle physics.
"The discovery of the Higgs boson at Cern last year, which validates the Brout-Englert-Higgs mechanism, marks the culmination of decades of intellectual effort by many people around the world."
Scotland's First Minister Alex Salmond also congratulated Prof Higgs, who is an emeritus professor at Edinburgh University.
He said: "Today, the Higgs boson, which carries his name, is a scientific discovery which is renowned the world over. This richly deserved honour not only highlights the quality of research carried out in Scotland, but also how science inspires us to look for answers to fundamental questions about life and the universe.
"Earlier this year Professor Higgs agreed to a new Scottish Government prize to be named in his honour, recognising the brightest young school physicists. His commitment to encouraging our next generation of scientists is well-known, and the first winners of the Higgs Prize will be announced later this year."
Prime Minister David Cameron tweeted: "Congratulations to Britain's Professor Peter Higgs, who is sharing this year's #NobelPrize for Physics."
Universities and Science Minister David Willetts Minister said: "I congratulate Professor Peter Higgs on his Nobel Prize. This is the 23rd Nobel Prize for Physics to come to the UK and continues a long tradition of scientific discovery.
"We should also celebrate the efforts of the thousands of scientists and engineers all over the world who have worked on the Large Hadron Collider and who have participated in the long search for the Higgs boson.
"Our new Nobel Laureate thoroughly deserves his prize. It's an incredible endorsement of the quality of UK science."
Dr Frances Saunders, president of the Institute of Physics, said: "The work undertaken to discover the Higgs - from the original theories to the construction of the world's most powerful particle-smasher - has led to a very exciting and productive period in physics research. It has been a long journey but one that has inspired a generation to engage with the subject.
"With the existence of the Higgs boson confirmed, explaining why the fundamental building blocks of nature acquire mass, we can now move on to the next challenges to our understanding such as the phenomena of dark matter and quantum gravity."
Professor Michael Duff, chair of theoretical physics at Imperial College London, said the Higgs boson theory will remain part of human understanding "for centuries".
He said: "I am delighted to hear that Peter Higgs and Francois Englert have won this year's Nobel Prize for Physics, which is richly deserved. Their seminal contributions, along with those of Tom Kibble here at Imperial College, explaining how elementary particles acquire a mass, form a vital part of the Standard Model of particle physics, pioneered by Imperial Nobel Laureate Abdus Salam.
"Their ideas in theoretical physics, vindicated in 2012 by the discovery at Cern of the Higgs boson, will persist as part of human understanding of the physical universe for centuries to come, long after today's stars of politics, business and entertainment have been forgotten."
The Princess Royal, in her role as chancellor of the University of Edinburgh, reflected on the Nobel announcement during an engagement at the university today.
She said: "As chancellor, I'm delighted because I can claim all sorts of benefits for the university (which is) hugely proud to have that connection with Professor Higgs."
She said she thought her predecessor in the role, the Duke of Edinburgh, would be "even more delighted" about the announcement.
"For all of us, it's really good news," she told the gathering.
The Duke recently met Prof Higgs during an August visit to the Royal Society of Edinburgh - Philip's first official engagement following an operation and period of convalescence.
In a fuller statement to add to his earlier tweet, the Prime Minister said: "This brilliant achievement is richly-deserved recognition of his lifetime of dedicated research and his passion for science. It is also a credit to the world-leading British universities in which this research was carried out, including the University of Edinburgh, Imperial and Kings College London.
"It took nearly 50 years and thousands of great minds to discover the Higgs Boson after Professor Higgs proposed it, and he and all those people should be extremely proud."
Imran Khan, chief executive of the British Science Association, joined the legions of well-wishers offering congratulations to Prof Higgs.
He said: "As well as deepening our understanding of the universe we live in, Higgs's prediction excited the public and captured our imaginations, taking us all on the same journey that the Cern scientists were on - we hope it will leave more people than ever interested and engaged with science."
Scots writer Ian Rankin tweeted: "Called Peter Higgs to congratulate him on his Nobel. Turned out he'd already heard my message. Physics, eh?"
Comedian Dara O'Briain tweeted: "I had the honour of interviewing Peter Higgs at Cheltenham Science Fest this year. A delightful man, couldn't be happier for him."
Professor Peter Higgs has journeyed to prominence along with the famous particle that bears his name.
Now at the age of 84, he is fast becoming a global celebrity as creator of the theory behind the ''God particle''.
But recognition was a long time in coming: the quiet physicist has been waiting for science to catch up with his ground-breaking ideas since 1964.
It was in that year he dreamed up the concept after a moment of inspiration while walking in the Cairngorms.
Two scientific papers followed, the second of which was initially rejected and then finally published in the respected journal Physical Review Letters.
Prof Higgs's groundbreaking proposal was that particles acquire mass by interacting with an all-pervading field spread throughout the universe. The more they interact, the more massive and heavy they become.
A ''boson'' particle was needed to carry and transmit the effect of the field.
His concept sparked a 40 year hunt for the Higgs boson which culminated last July when a team from the European nuclear research facility at Cern in Geneva announced the detection of a particle that fitted the description of the elusive Higgs.
Scientists used the world's biggest atom smashing machine, the Large Hadron Collider on the Swiss-French border, to track down the missing particle.
Peter Higgs was born in Newcastle in 1929, the son of a BBC sound engineer.
After his family moved to Bristol, he proved a brilliant pupil at Cotham Grammar School before going on to read theoretical physics at King's College London.
He was awarded first class honours in 1950, and after failing to secure a lectureship at King's College, set off for Scotland and the University of Edinburgh.
Prof Higgs retired from this post in 2006 and assumed the title of emeritus professor.
His contribution to physics has long been recognised within the scientific world - with eight honorary degrees and dozens of academic prizes since the 1980s.
Never one to blow his own trumpet, the scientist is described by friends and colleagues as ''very unassuming'' and shy.
Some believe his retiring nature may even have held back his career.
But despite his best efforts to keep a low profile, he now finds himself in the spotlight: autograph hunters have even started to approach him in the street.
Last year he missed out on a Nobel prize but the professor was made a Companion of Honour in the New Year Honours list.
The accolade confers no title but only a select group are rewarded with it for achievements in the arts, literature, music, science, politics, industry, or religion.
Prof Higgs remained typically humble when his honour was announced. ''It's very nice to be right sometimes,'' he said.