Ripples in the fabric of space itself known as gravitational waves (pictured) were identified by a specially designed telescope at the south pole.
Like a cosmic tsunami, they were generated when the universe suddenly exploded into existence almost 14 billion years ago.
Scientists believe the cosmos expanded at an enormous rate - faster than the speed of light - in the first tiny fraction of a second after the Big Bang.
The theory, called "inflation", was dreamed up to explain why the universe today is so remarkably uniform.
Today's announcement from the Harvard-Smithsonian Center for Astrophysics in the US provides the first direct "smoking gun" evidence of inflation.
It also challenges scientists to grapple with a new mystery, because no-one can yet explain how inflation happened.
The signal detected by the BICEP2 (Background Imaging of Cosmic Extragalactic Polarazation) telescope is much stronger than expected.
"This has been like looking for a needle in a haystack, but instead we found a crowbar," said team co-leader Dr Clem Pryke, from the University of Minnesota.
Rumours about the discovery had been rife in the world of astrophysics. To make sure they got it right, the scientists analysed their data for more than three years before making it public.
If the findings are independently confirmed, members of the BICEP2 team are likely to be in the running for a Nobel Prize.
British expert Dr Ed Daw, from the University of Sheffield, said: "Gravitational waves emitted at the time of the big bang can tell us how the universe came to exist.
"If these results prove correct, we will have new key information on the very early Universe, information that is hard to get from any other source."
Gravitational waves were predicted in Albert Einstein's General Theory of Relativity. Their potential sources include super-dense neutron stars and black holes, as well as the Big Bang. However, until now they have never been seen directly.
BICEP2 looked for an imprint of primordial gravitational waves in the cosmic microwave background (CMB), a faint radiation afterglow left over from when the universe was just 400,000 years old.
"Our team hunted for a special type of polarization called 'B-modes' which represents a twisting or 'curl' pattern in the polarized orientations of the ancient light," said one of the lead scientists Professor Jamie Bock, from the California Institute of Technology.
The swirly B-mode pattern provided a unique gravitational wave signature.
"This is the first direct image of gravitational waves across the primordial sky," said team member Professor Chao-Lin Kuo, from Stanford University in California.
Astrophysicist Professor Avi Loeb, from Harvard University, said: "This work offers new insights into some of our most basic questions: Why do we exist? How did the universe begin? These results are not only a smoking gun for inflation, they also tell us when inflation took place and how powerful the process was."
Leading British astrophysicist Dr Chris Lintott, from Oxford University, said: "This could be the most significant discovery for years, it's hugely exciting.
"It's exciting for observers because it provides a new window on a very early stage of the universe's evolution, and its exciting for theorists because we might now finally have a handle on what sort of thing caused inflation.
"At the moment there are lots of competing ideas but until now we haven't had the data to test them against.
"What's interesting is that the 'smoking gun' proved much more obvious than a lot of people thought it would be. It raises the possibility of several other experiments confirming the finding."
Direct evidence of inflation has some profound implications, said Dr Lintott. For instance, it points to a deep connection between the subatomic world of quantum mechanics and the cosmic-scale of general relativity.
At the quantum level, subatomic particles pop in and out of existence even in empty space.
Inflation may have blown up these quantum fluctuations, turning them into the seeds of galaxies.
Professor John Womersley, chief executive of the Science and Technology Facilities Council (STFC) which funds UK cosmology research, said: "Modern cosmology is based on three underlying assumptions - inflation, dark matter and dark energy. We don't know what any of them actually are, but over the last few years we have seen increasingly strong evidence that they are real.
"Today's announcement from the Bicep project continues that process. Inflation is the very rapid expansion of the very early universe that is one of the pillars of our understanding of cosmology. Without inflation we would not be here.
"A detection of primordial B-mode polarisation provides very strong evidence for inflation and, if the Bicep results are verified by other experiments, that will be what we have.
"With the recent confirmation of the existence of the Higgs boson and now the first direct evidence for inflation, these are very exciting times to be a physicist."
BICEP2 was the second stage of the mission to detect gravitational waves.
The scientists travelled to the South Pole to take advantage of its cold, dry, stable air.
"The South Pole is the closest you can get to space and still be on the ground," said principal investigator Professor John Kovac, from the Harvard-Smithsonian Centre for Astrophysics.
"It's one of the driest and clearest locations on Earth, perfect for observing the faint microwaves from the Big Bang."
The scientists acknowledge that interaction between CMB and space dust could produce a similar effect as that produced by primordial gravitational waves. But they have made painstaking efforts to rule out such a possibility.