ESA Director General Jean-Jacques Dordain called the landing "a big step for human civilization."
"We are sitting on the surface and Philae is talking to us," said Stephan Ulamec, the Philae lander manager. "We are on the comet."
Although a thruster malfunctioned, the mission was not severely impacted, the ESA said.
"The cold gas thruster on top of the lander does not appear to be working, so we will have to rely fully on the harpoons at touchdown," Ulamec said in an ESA blog post. "We'll need some luck not to land on a boulder or a steep slope."
The comet, which is about 4 billion miles from the Earth, could hold important remnants of the ancient universe, scientists say.
"We can investigate about all the building blocks of our solar system, and it will probably help us to answer fundamental questions about the origins of our life," said Daniel Neuenschwander of the Swiss delegation to the ESA.
The comet was first observed in 1969 and is named for its discoverers, Klim Churyumov and Svetlana Gerasimenko.
"Like all comets, it has a fairly small, solid nucleus which is thought to resemble a dirty snowball," the ESA said on its website.