The European Space Agency (ESA) received the all-clear message "Hello World!" from its Rosetta spacecraft, 500 million miles away, shortly after 6pm.
Rosetta was put into hibernation 31 months ago to conserve energy for its long journey to meet comet 67P/Churyumov-Gerasimenko.
The spacecraft, launched by the ESA from Kourou in French Guiana nearly 10 years ago, is on a historic mission to drop a lander on the icy surface of a comet.
One of its first tasks will be to search for a suitable landing site for the box-like Philae lander, which will drill samples from the ground for analysis.
Philae will also capture panoramic images of the view from the comet's surface with an on-board camera.
Scientists hope Rosetta will answer important questions about the origins of the Solar System and the way comets evolve and develop.
Rosetta was put to sleep as it headed to regions as distant as the planet Jupiter, where the Sun's weak rays provide only limited amounts of energy.
Unlike other long-distance space probes, the craft has no nuclear batteries and instead relies on electricity generated by ultra-sensitive 15-metre long solar panels.
To make certain Rosetta woke up, the craft was fitted with not one but four quartz "alarm clocks".
The wake-up procedure involved switching on the probe's star-tracker navigation system, slowing its spin and warming up electrical components. This allowed Rosetta to orientate itself towards the Earth and start transmitting.
Scientists at the American space agency Nasa's 70-metre-wide deep space dish at Goldstone, California, were listening out for the extremely weak signal and relayed it to ESA.
Rosetta has already travelled round the Sun five times, picking up energy from the gravitational "slingshot" effect of Earth and Mars.