Philae, the first spacecraft to land on a comet, was dropped on to the surface of Comet 67P by its mothership, Rosetta, last November.
It worked for 60 hours before its solar-powered battery ran flat.
The comet has since moved nearer to the Sun and Philae has enough power to work again, says the BBC’s science correspondent Jonathan Amos.
Esa said Philae had contacted Earth, via Rosetta, for 85 seconds on Saturday in the first contact since going into hibernation in November.
“Philae is doing very well. It has an operating temperature of -35C and has 24 watts available,” said Philae project manager Stephan Ulamec.
Scientists say they now waiting for the next contact.
ESA scientist Mark McCaughrean told the BBC: “It’s been a long seven months, and to be quite honest we weren’t sure it would happen – there are a lot of very happy people around Europe at the moment.”
Philae was carrying large amounts of data that scientists hoped to download once they made contact again, he said.
“I think we’re optimistic now that it’s awake that we’ll have several months of scientific data to pore over,” he added.
This is one of the most astonishing moments in space exploration and the grins on the faces of the scientists and engineers are totally justified, says BBC science editor David Shukman.
For the first time, we will have a hitchhiker riding on a comet and describing what happens to a comet as it heats up on its journey through space, he adds.
‘Building blocks of life’
Philae is designed to analyse the ice and rocky fragments that make up the comet.
Professor Monica Grady from the Open University told the BBC that scientists now hoped to be able to carry out experiments to see whether comets were the source of life on Earth.
Comets contained a lot of water and carbon, and “these are the same sorts of molecules responsible for getting life going,” she said.
“What we’re trying to find out is whether the building blocks of life, in terms of water and carbon-bearing molecules, were actually delivered to Earth from comets.”