If any one of those operations had failed, the probe would have gone whizzing past its target.
The final maneuver was a small firing of thrusters, lasting just six minutes and 26 seconds, it said.
"This burn will tip Rosetta into the first leg of a series of three-legged triangular paths about the comet," ESA said.
The "pyramidal" track placed the craft at a height of about 60 miles above the comet, said Lodiot.
- Primeval matter -
Each leg of the triangle will be around 60 miles and take Rosetta between three and four days to complete. Rosetta will gradually reduce its height, entering gravitational orbit in September.
Comets are believed by astrophysicists to be ancient ice and dust left from the building of the Solar System around 4.6 billion years ago. This cosmic rubble is the oldest, least touched material in our stellar neighborhood.
Understanding its chemical ID and physical composition will give insights into how the planets coalesced after the Sun flared into light, it is hoped.
It could also determine the fate of a theory called "pan-spermia," which suggests comets, by smashing into the infant Earth, sowed our home with water and precious organic molecules, providing us with a kickstart for life.
The spacecraft is named after the famous stone, now in the British Museum, which explained Egyptian hieroglyphics, while its payload, Philae, is named after a Nile obelisk that in turn helped decipher the Rosetta stone.
The 2.5-mile comet returns around the Sun on an egg-shaped orbit every six and a half years, its furthest point being beyond Jupiter.
It is named after two Ukrainian astronomers, Klim Churyumov and Svetlana Gerasimenko, who first spotted it in 1969.