She was greeted with applause and cheers by around 200 people, mainly employees, outside the centre on Aberdeen Royal Infirmary's Foresterhill campus which provides emergency care and support for cancer, heart and blood patients.
Lord Provost George Adam, in his role as Her Majesty's Lord Lieutenant, met the royal visitor on her arrival.
The Queen, who was wearing pink, was given a tour of the £110 million facilities and met staff and patients at the centre.
She was taken round the haematology, oncology and radiology units which have been brought together in the centre to improve links between the departments.
She was introduced to Susan Crean Smith, 55, from Dufftown in Aberdeenshire, and Keiran MacRonald, 16, from Aberdeen, who are both receiving cancer treatment.
The Queen then visited the emergency department to see a state-of-the art CT scanner then unveiled a plaque to mark her visit and to officially open the centre.
The Queen also met representatives from the Friends of Anchor charity which raises money for the haematology, oncology and radiology unit.
Patients being treated there came to the doorway of their rooms, some using walking frames or wheelchairs, to catch a glimpse of the Queen, who nodded and smiled as she passed them.
Dr Angus Cooper, consultant of emergency medicine and clinical lead for the emergency care centre project, said it is a "great honour" to welcome the Queen.
He showed her the facilities at the centre, which started treating patients in December last year, and said that on a busy weekend day between 400 and 450 patients could be seen.
"The facilities are tremendous. We've also thought about how we put it together from the point of view of the patients," Dr Cooper said.
"For example, the Queen was shown today the CT scanner which is right by the door where the most seriously ill and injured patients come into the hospital and it is 10 yards for us to take people to the CT scanner.
"It's been nearly seven years putting this together, so it's tremendous to see it all come together and it's a tremendous honour for the Queen to officially open it."
The centre is the biggest development at the site since the hospital was built in 1936.
According to NHS Grampian, it will improve privacy, cut the length of stays and lower the risk of infection.
The new building, named after Matthew Hay, medical officer for Aberdeen City in the 1920s who created the Foresterhill campus, has 350 beds and hosts the accident and emergency unit as well as the regional NHS24 services.
Before the Queen unveiled the plaque, local councillor Bill Howatson, who is chairman of the health board, addressed the room of around 50 guests.
He complimented the efforts of hundreds of people who worked "tirelessly" to bring the centre into existence.
"This facility, Your Majesty, is much more than a building. Every step of the way, the patients, their families', carers and friends have been absolutely at the centre of what has been created here. The values of NHS Grampian - caring, listening and improving - have guided this project and have produced something very special," he said.
"We have a vision of healthcare in the north-east and we are delivering that vision. This building is the prime example of what we can deliver."
Mr Howatson then invited the Queen to reveal the plaque and presented her with a numnah - a cushion for under a horse's saddle - which had been decorated with the NHS Grampian tartan.
The Queen signed a visitors' book and outside met members of rapid response car team, made up of accident and emergency doctors.
Earlier, she visited the International School of Aberdeen, which has around 500 pupils from 39 countries, where she watched a performance by pupils in the school's newly built Queen Elizabeth Theatre. She met staff and pupils, unveiled a plaque and signed the visitors' book.
The international school was founded in 1972 and teaches pupils from nursery all the way through to secondary level.