He lifted his arms in victory shortly after landing, setting off loud cheers from jubilant onlookers and friends inside the mission's control centre in Roswell, New Mexico.
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It was the highest-ever jump for a skydiver, though it was not immediately certain whether Baumgartner had broken the speed of sound during his free-fall, which was one of the goals of the mission. Organisers said the descent lasted for just over nine minutes, about half of it in free-fall.
Three hours earlier, Baumgartner, known as "Fearless Felix," had taken off in a pressurised capsule carried by a 55-storey ultra-thin helium balloon. After an at-times tense ascent, which included concerns about how well his facial shield was working, the 43-year-old former military parachutist completed a final safety check-list with mission control.
As he exited his capsule from high above Earth, he flashed a thumbs-up sign, well aware that the feat was being shown on a live-stream on the internet with a 20-second delay.
During the ensuing jump - from more than three times the height of the average cruising altitude for jetliners - Baumgartner was expected to hit a speed of 690 mph.
Any contact with the capsule on his exit could have torn his pressurised suit, a rip that could expose him to a lack of oxygen and temperatures as low as minus 70 degrees Fahrenheit (minus 57 degrees Celsius). That could have caused lethal bubbles to form in his bodily fluids.
But none of that happened. He activated his parachute as he neared Earth, gently gliding into the desert east of Roswell and landing without any apparent difficulty. He then was taken by helicopter to meet fellow members of his team, whom he hugged in celebration.
Coincidentally, Baumgartner's attempted feat also marked the 65th anniversary of US test pilot Chuck Yeager's successful attempt to become the first man to officially break the sound barrier aboard an airplane.
At Baumgartner's insistence, some 30 cameras on the capsule, the ground and a helicopter recorded the event. While it had been pegged as a live broadcast, organisers said was actually under a 20-second delay in case of a tragic accident.
Shortly after launch, screens at mission control showed the capsule as it began rising high above the New Mexico desert, with cheers erupting from organisers. Baumgartner could be seen on video, calmly checking instruments inside the capsule.
Baumgartner's team included Joe Kittinger, who first attempted to break the sound barrier from 19.5 miles up in 1960, reaching a speed of 614 mph, just under the sound barrier. With Kittinger inside mission control today, the two men could be heard going over technical details during the ascension.
"Our guardian angel will take care of you," Kittinger radioed to Baumgartner around the 100,000-foot mark. Kittinger noted that, it was getting "really serious" now.
An hour into the flight, Baumgartner had ascended more than 63,000 feet and had gone through a trial run of the jump sequence that will send him plummeting toward Earth. Ballast was dropped to speed up the ascent.
Kittinger told him, "Everything is in the green. Doing great."
As Baumgartner ascended in the balloon, so did the number of viewers watching on YouTube. Nearly 7.3 million watched as he sat on the edge of the capsule moments before jumping. After he landed, Red Bull posted a picture of Baumgartner on his knees on the ground to Facebook, generating nearly 216,000 likes, 10,000 comments and more than 29,000 shares in less than 40 minutes.
On Twitter, half the worldwide trending topics had something to do with the jump, pushing past seven National Football League games.
Among the tweets was one from NASA: "Congratulations to Felix Baumgartner and RedBull Stratos on record-breaking leap from the edge of space!"
This attempt, sponsored by the energy drink maker Red Bull, marked the end of a five-year road for Baumgartner, a record-setting high-altitude jumper. He had already made two preparation jumps in the area, one from 15 miles high and another from 18 miles high. It will also be the end of his extreme altitude jumping career; he has promised this will be his final jump.
Baumgartner has said he plans to settle down with his girlfriend and fly helicopters on mountain rescue and firefighting missions in the US and Austria.
Dr Jonathan Clark, Baumgartner's medical director, had told reporters he expected the pressurised spacesuit to protect him from the shock waves of breaking the sound barrier. A successful jump could lead NASA to certify a new generation of spacesuits for protecting astronauts and provide an escape option from spacecraft at 120,000 feet, he said.
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