Dark matter - which does not emit or reflect enough light to be "seen" - is thought to make up 25% of the Universe.
By contrast, the ordinary matter we can see is believed to make up no more than about 5% of our Universe.
Until now, astronomers have only been able to infer the existence of this dark material through the gravitational effects it has on ordinary matter.
What the researchers have done is, in effect, to identify the gravitational "signature" of dark matter.
This signature was created by dark matter and ordinary matter being wrenched apart by the immense collision of two large galaxy clusters.
"The kinetic energy of this collision is... enough to completely evaporate and pulverise planet Earth ten trillion, trillion times over," said team member Maxim Markevitch, of the Harvard-Smithsonian Center for Astrophysics in Cambridge, US.
Study leader Doug Clowe, from the University of Arizona, said: "This provides the first direct proof that dark matter must exist and that it must make up the majority of the matter in the Universe."
Astronomers have known since the 1930s that these galaxy clusters have far too much gravity to be explained by the amount of visible matter in them alone.
This extra gravity has two possible explanations. One is that most matter in the clusters is in a form we cannot see, because it does not absorb or emit light. A second explanation is that gravity does not behave the same way in galaxy clusters light-years in size as it does on Earth.
But in the cosmic smash-up (the colliding feature is known to astronomers as the Bullet Cluster), these components have been pulled apart. The astronomers were lucky enough to catch the collision just 100 million years after it occurred - the blink of an eye in cosmic time.
The researchers could see that the hot gas in the collision had been slowed down by a drag force, similar to air resistance. Meanwhile, the galaxies themselves continued speeding through space, leaving the gas behind.
Dark matter particles should not slow down in the same way as the gas; they do not interact directly with themselves or the gas except through gravity. Instead, dark matter should behave in a similar way to the galaxies.
More mass in gas
If dark matter did exist, the astronomers expected to find the majority of mass in clusters residing around the galaxies. But if dark matter did not exist, most of the galaxy clusters' mass would be in its diffuse hot gas. This is because galaxy clusters typically contain 10 times as much ordinary mass in gas as in stars. The researchers found most of the mass was located near the galaxies - ahead of the gas clouds - showing the dark matter really was there. The majority of the Universe - some 70% - is composed of dark energy, an equally mysterious quantity which exerts negative pressure.
"Dark matter and dark energy are not what anyone would have expected starting from the perspective of what the Universe should be like," said Sean Carroll, a cosmologist at the University of Chicago, who was not involved with the study, "but we're trying to understand why it's like that and this result puts us on that path."
Marusa Bradac, at the Stanford Linear Accelerator Center (Slac) in California, added: "We had predicted the existence of dark matter for decades, but now we've seen it in action. This is groundbreaking."
In order to locate the mass in the clusters, researchers used the Chandra and Hubble space telescopes, along with the Very Large Telescope and Magellan optical telescopes in Chile.
This was done by measuring the effect of gravitational lensing, where gravity from the clusters distorts light from background galaxies, as predicted by Einstein's theory of general relativity.