It is the first time a soft landing has been achieved on a comet -- but there was a hitch.
Comet 67P has a very weak gravity, so anchoring harpoons were designed to shoot into the comet to fix the spacecraft to the surface. They failed to fire and Philae is not firmly secure, ESA says.
Philae lander manager Stephan Ulamec said the probe may have lifted off again and turned.
"So maybe we didn't land once -- we landed twice," he told a news conference.
"Did we land in a soft sandbox or is there something else happening? We don't fully understand what happened," he said.
Ulamec said scientists remain upbeat as they are still receiving data from the spacecraft and they hope to learn more Thursday.
Shortly after landing was confirmed, the probe tweeted: "Touchdown! My new address: 67P!" Later, it tweeted again: "I'm on the surface but my harpoons did not fire."
Led by ESA with a consortium of partners including NASA, scientists on the Rosetta comet-chasing mission hope to learn more about the composition of comets and how they interact with the solar wind -- high energy particles blasted into space by the sun.
Speaking to CNN shortly after the landing, ESA lander system engineer Laurence O'Rourke said they were trying to check the orientation of the craft, to see "how we landed and where we landed."
"We are extremely happy," he said. "To get the signal it had touched the surface was a major achievement -- it was quite extraordinary. Philae is already taking measurements, sniffing the comet."
He also said the probe could start drilling into the surface and analyzing the material as soon as Thursday.
The comet is currently 500 million kilometers (310 million miles) from Earth and pictures from the Rosetta mission to track it on its orbit around the sun have amazed scientists.
NASA's chief scientist, Ellen Stofan, told CNN: "That comet is the most bizarre, wonderful thing I have ever seen. Those images have just blown me away. Philae was such a huge success before it even did anything, so kudos to ESA and the scientific community.
"No one has ever gotten data like Rosetta has gotten. No one has ever been able to land on a comet the way Philae just did."
Astronomer Robert Massey also called the landing a tremendous achievement.
"A comet is a bit like a time capsule, which is why it's special," he told CNN.
"It's an insight into the composition of the early solar system -- the ratio of chemicals.
"Even without Philae, we still have Rosetta in orbit around a comet, giving the ability to watch it at close quarters. There will be a lot of science from this," he said.
Weighing in at 220 pounds, it might be the size of a domestic washing machine but Philae is considerably smarter.
It is equipped with an array of experiments to photograph and test the surface of Comet 67P as well as finding out what happens when the roasting effect of the sun drives off gas and dust.
Built by a European consortium, led by the German Aerospace Research Institute (DLR), the landing probe has nine experiments.
According to details on ESA's Rosetta website, sensors on the lander will measure the density and thermal properties of the surface, gas analyzers will help to detect and identify any complex organic chemicals that might be present, while other tests will measure the magnetic field and interaction between the comet and solar wind.
Philae also carries a drill that can drive 20 centimeters (8 inches) into the comet and deliver material to its on-board ovens for testing.
Scientists are already pleased with progress of the mission.
ESA project scientist Matt Taylor said: "The orbiter will remain alongside the comet for over a year, watching it grow in activity as it approaches the sun, getting to within 180 million kilometers (112 million miles) in summer next year, when the comet will be expelling hundreds of kilograms of material every second.
"It's got an awesome profile -- the adventure of the decade-long journey necessary to capture its prey, flying past the Earth, Mars and two asteroids on the way," he said.
Daniel Brown, an astronomy expert at Nottingham Trent University in the UK, said: "Although we have landed on planets, moons and asteroids, it has never been attempted for a nucleus of a comet -- and with good reason. These objects have a very low gravity, are loosely composed of ice, dust and rocks, and are very irregular in shape. They are temperamental in their behavior and notoriously difficult to predict.
"Comets such as 67P have already been exposed to the intense heat of the sun in their past orbits, resulting in their surface being altered, but going beneath the surface will give us an insight into unchanged material, allowing us to peak into the chemical composition of our early solar system.
"Apart from the amazing scientific results, the sheer challenge and ambition of such a mission is outstanding and illustrates how our space exploration of the solar system has become more advanced and successful. It gives us much to hope for in future missions."
And science fiction writer Alastair Reynolds said: "This is science fiction made real in terms of the achievement of the mission itself, but Rosetta is also taking us a step closer to answering science fiction's grandest question of all: Are we alone?"