"When I was standing there on top of the world, you become so humble, you do not think about breaking records anymore, you do not think about gaining scientific data," he said after the jump. "The only thing you want is to come back alive."
A worldwide audience watched live on the Internet via cameras mounted on his capsule as Baumgartner, wearing a pressurized suit, stood in the doorway of his capsule, gave a thumbs-up and leapt into the stratosphere.
"Sometimes we have to get really high to see how small we are," an exuberant Baumgartner told reporters outside mission control after the jump.
Baumgartner's descent lasted for just over nine minutes, about half of it in a free fall of 119,846 feet, according to Brian Utley, a jump observer from the International Federation of Sports Aviation. He said the speed calculations were preliminary figures.
Baumgartner said traveling faster than sound is "hard to describe because you don't feel it."
With no reference points, "you don't know how fast you travel," he said.
The 43-year-old former Austrian paratrooper with more than 2,500 jumps behind him had taken off early Sunday in a capsule carried by a 55-story ultra-thin helium balloon.
His ascent that was tense at times and included concerns about how well his facial shield was working.
Any contact with the capsule on his exit could have torn his suit, a rip that could expose him to a lack of oxygen and temperatures as low as minus-70 degrees. 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. The images triggered another loud cheer from onlookers at mission control, among them his mother, Eva Baumgartner, who was overcome with emotion, crying.
He then was taken by helicopter to meet fellow members of his team, whom he hugged in celebration.
Coincidentally, Baumgartner's feat came on the 65th anniversary of the day that U.S. test pilot Chuck Yeager became the first man to officially break the sound barrier in a jet.
At Baumgartner's insistence, some 30 cameras recorded his stunt Shortly after launch, screens at mission control showed the capsule as it began rising high above the New Mexico desert, with cheers erupting from organizers. Baumgartner could be seen on video, calmly checking instruments inside the capsule.
Baumgartner's team included Joe Kittinger, who first tried to break the sound barrier from 19.5 miles up in 1960, reaching speeds of 614 mph. With Kittinger inside mission control, 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.
An hour into the flight, Baumgartner had ascended more than 63,000 feet and had gone through a trial run of the jump sequence. Ballast was dropped to speed up the ascent.
Kittinger told him, "Everything is in the green. Doing great."
As Baumgartner ascended, 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, his sponsor, 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 NFL football games. Among them was this tweet from NASA: "Congratulations to Felix Baumgartner and RedBull Stratos on record-breaking leap from the edge of space!"
This attempt marked the end of a five-year road for Baumgartner, a record-setting high-altitude jumper. He already made two preparation jumps in the area, one from 15 miles high and another from 18 miles high. He has said that this was 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 U.S. and Austria.