They have observed the warping of space-time generated by the collision of two black holes more than a billion light-years from Earth.
The international team says the first detection of these gravitational waves will usher in a new era for astronomy.
It is the culmination of decades of searching and could ultimately offer a window on the Big Bang.
The collaboration operates a number of labs around the world that fire lasers through long tunnels, trying to sense ripples in the fabric of space-time.
Expected signals are extremely subtle, and disturb the machines, known as interferometers, by just fractions of the width of an atom.
But the black hole merger was picked up by two widely separated LIGO facilities in the US.
The merger radiated three times the mass of the sun in pure gravitational energy.
“We have detected gravitational waves,” Prof David Reitze, executive director of the LIGO project, told journalists at a news conference in Washington DC.
“It’s the first time the Universe has spoken to us through gravitational waves. Up until now, we’ve been deaf.”