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Rosetta, which was launched by the European Space Agency (ESA) in 2004, is due to rendezvous with comet 67P/Churyumov-Gerasimenko and land a probe on it this year in an unprecedented manoeuvre.
Scientists hope data the probe gathers will allow them to peek into a kind of astronomical time capsule that has preserved for millions of years clues as to what the world looked like when our solar system was born.
"Since comets are so primitive, they can give scientists a chance to understand how the solar system formed, where it came from," Rosetta spacecraft operations manager Andrea Accomazzo told Reuters ahead of the wake-up call.
On its way to the comet, a roughly 3 by 5 km-large rock discovered in 1969, Rosetta has been circling the sun on a widening spiral course, swinging past Earth and Mars to pick up speed and adjust its trajectory.
The mission will perform several historical firsts, including the first time a spacecraft orbits a comet rather than just whizzing by it to snap some fly-by pictures, and the first time a probe has landed on a comet's nucleus.
Rosetta is also the first mission to venture beyond the main asteroid belt relying solely on solar cells for power generation, which is also why it had to be put into a deep sleep for 957 days.
"It has been so far away from the sun that the solar rays were not able to generate enough energy to safely operate the spacecraft," said Accomazzo, who has been working on the Rosetta mission since 1997.
Accomazzo is based at the ESA's satellite operations in the German town of Darmstadt, south of Frankfurt.
Having neared the sun again as it tracks the comet on its elliptical orbit around the sun, Rosetta was gently awakened by its internal alarm clock at 1000 GMT on Monday. It then warmed up its systems and transmitted a sign of life - a radio signal - to its creators on Earth.
Once it is fully up and running, it will start to approach the comet. By August, it should catch up with it and land its probe on it in November.
Until the end of 2015, the probe will gather data on the comet's surface and examine how it changes as its nears the sun.