The incredible trip, launched on March 2, 2004, marks a milestone in mankind's effort to understand the mysterious 'shooting stars' that periodically flash past Earth, and which have often been viewed with fear and trepidation.
While the moon, Mars and even asteroids have been visited, no spacecraft has yet gotten so close to a comet. Having achieved this feat, Rosetta will go one step further and drop a lander on 67P's icy surface a maneuver planned for November.
"You can compare what we've done so far to finding a speck of dust in a big city," said Gerhard Schwehm, who was lead scientist on the Rosetta mission until his recent retirement.
That's probably an understatement.
To catch their quarry, scientists at the European Space Agency had to overcome a series of hurdles that included a last-minute change of destination after a carrier rocket failure delayed launch and a tense hibernation period of 31 months during which the probe was out of contact with ground stations.
Before Rosetta swung alongside 67P with a final thrust Wednesday, the spacecraft also had to accelerate to 55,000 kph (34,000 mph) a speed that required three loops around Earth and one around Mars.
Underlining the singular achievement, ESA's director-general Jean-Jacques Dordain told scientists and spectators at the mission control center in Darmstadt, Germany: "This is your only chance to have a rendezvous with a comet."
Rosetta will now spend several months observing 67P from a safe distance of up to 100 kilometers (60 miles). This will give scientists time to find a safe place to land Rosetta's sidekick, Philae.
This maneuver will pose an unprecedented challenge because there will be no second shot. Recent pictures of 67P show that its surface is porous, with steep cliffs and house-sized boulders.
One person involved with Rosetta from the start told The Associated Press that the landing was "mission impossible" with only a slim chance of success. He spoke on condition of anonymity to avoid harming his employer.
Even if the landing fails, Rosetta itself will remain in the comet's orbit until at least the end of 2015, gathering reams of data with its 11 on-board sensors. As 67P gets closer to the sun it will begin to fizz and release the cloud of dust and ice that most people associate with comets.
"We're going to have a ringside seat to see, for the first time, a comet turn into a comet, to develop its tail and explain what for centuries mankind has been puzzled by," said David Southwood, a former president of the Royal Astronomical Society who was involved with the Rosetta mission from the start.
Overall, scientists hope the ?1.3 billion ($1.74 billion) mission will help them learn more about the origins of comets, stars, planets and maybe even life on Earth, he said.
Mark McCaughrean, a senior scientific advisor at ESA, predicted plenty of surprises ahead.
"With this comet, every time we see a new image the jaws drop," he said. "Everybody just can't believe how lucky we have been."
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Comet probe timeline
Darmstadt, Germany • Europe's unmanned space probe Rosetta completed a decade-long journey on Wednesday to link up with a comet. The probe will orbit and study the giant ball of dust and ice as it hurtles toward the sun before attempting to drop a lander onto the comet in the coming months.
Here's a look at key moments during Rosetta's incredible trip:
March 2, 2004: Europe's unmanned probe Rosetta takes off from Kourou, French Guiana, after a series of delays, including an abandoned January 2003 launch window because of a rocket problem.
Feb. 25, 2007: Rosetta carries out a close flyby of Mars. European Space Agency's mission control breaks out in applause after the end of 15 tense minutes of radio silence as the craft passes behind the Red Planet.
Sept. 5, 2008: Probe successfully passes close to an asteroid 250 million miles from Earth. The spacecraft loses its radio signal for 90 minutes as planned during the flyby of the Steins asteroid, also known as Asteroid 2867.
July 10, 2010: Between Mars and Jupiter, Rosetta transmits its first pictures from the largest asteroid ever visited by a satellite after it flies by Lutetia as close as 1,900 miles (3,200 kilometers). It is the closest look to date of the Lutetia asteroid.
Jan. 20, 2014: Waking after almost three years of hibernation, Rosetta sends its first signal back to Earth, prompting cheers from scientists. Systems had been powered down in 2011 to conserve energy, leaving scientists in the dark for 31 months.
Aug. 6, 2014: Rosetta swings alongside comet 67P/Churyumov-Gerasimenko somewhere between the orbits of Mars and Jupiter.
November 2014: The probe will try to drop a lander on the comet's icy surface.