The Juno satellite, which left Earth five years ago, had to fire a rocket engine to slow its approach to the planet and get caught by its gravity.
A sequence of tones transmitted from the spacecraft confirmed the braking manoeuvre had gone as planned.
Receipt of the radio messages prompted wild cheering at Nasa's mission control in Pasadena, California.
"All stations on Juno co-ord, we have the tone for burn cut-off on Delta B," Juno Mission Control had announced. "Roger Juno, welcome to Jupiter."
Scientists plan to use the spacecraft to sense the planet's deep interior. They think the structure and the chemistry of its insides hold clues to how this giant world formed some four-and-a-half-billion years ago.
Engineers had warned in advance that the engine firing was fraught with danger.
No previous spacecraft has dared pass so close to Jupiter; its intense radiation belts can destroy unprotected electronics.
One calculation even suggested the orbit insertion would have subjected Juno to a dose equivalent to a million dental X-rays.
But the probe is built like a tank with titanium shielding, and the 35-minute rocket burn appeared to go without a hitch.
While the radiation dangers have not gone away, the probe should now be able to prepare its instruments to start sensing what lies beneath Jupiter's opaque clouds.
Tuesday's orbit insertion has put Juno in a large ellipse around the planet that takes just over 53 days to complete.
A second burn of the rocket engine in mid-October will tighten this orbit to just 14 days. It is then that the science can really start.
This will involve repeat passes just a few thousand kilometres above the cloudtops.
At each close approach, Juno will use its eight remote sensing instruments - plus its camera - to peer down through the gas planet's many layers, to measure their composition, temperature, motion and other properties.
A priority will be to determine the abundance of oxygen at Jupiter. This will be bound up in its water.
"How much water Jupiter has tells us a lot about where the planet formed early in the Solar System," explained team-member Candy Hansen.
"We think that Jupiter may not have formed where it is today, and if it formed further away or closer in - that tells us a lot about how the Solar System in general formed. Because when we look at planets around other stars we see quite a menagerie of possibilities."