"Philae is talking to us," said Stephan Ulamec, the lander's manager. "We are on the comet."
"We definitely confirm that the lander is on the surface," said Andrea Accomazzo, flight operations director. "We can't be happier than what we we are now."
"This is a big step for human civilization," ESA president Jean-Jaques Dourdain said.
"The biggest problem of success is that it looks easy, especially for us who are not doing anything.
"When you know the sum of expertise, of dedication, of teamworking between 20 nationalities, of member states in Europe, plus co-operation with international partners.
"This type of success comes from hard work and expertise.
"Today we have demonstrated that the European expertise is the best expertise of the world. We are the first to have done that, and that will stay forever."
"This is truly epochal," said Hesse first minister Volker Bouffier. "On this day, Darmstadt is the middle of the space agency, and we are very proud here in Hesse and in Darmstadt."
"Congratulations to all of the scientists and engineers who have made the landing a success," said Birgitte Zypries, head of aerospace at the German Economic Ministry.
"We are hoping for nothing more, nothing less, than to find out more about the formation of our solar system."
"No single nation alone can realize a mission of this scale. We can only do it by working together."
News of the probe's safe arrival came via a live video feed from the control room and via Twitter.
The probe separated from its Rosetta mothership on Wednesday morning after all its systems were cleared to go earlier in the day.
A science lab bearing 10 instruments, Philae separated from its mother ship Rosetta at 0835 GMT to head towards Comet 67P/Churyumov-Gerasimenko, the agency said, after the last of four checks.
Final Go/NOGO complete! I We're GO for separation!!! pic.twitter.com/oYG3NBgdaJ— ESA Rosetta Mission (@ESA_Rosetta) 12. November 2014