Bezos and his crewmates touched down in the West Texas desert at the end of the more than 10-minute flight on Blue Origin’s New Shepard rocket on the 52nd anniversary of the Apollo 11 moon landing.
"Well done Blue Origin and Jeff Bezos, Mark, Wally and Oliver. Impressive! Very best to all the crew from me and all the team at Virgin Galactic," Branson, who recently completed his own spaceflight, tweeted.
The Blue Origin founder was accompanied by his brother, Mark, 18-year-old Oliver Daemen of the Netherlands, and an 82-year-old aviation pioneer Wally Funk – the youngest and oldest people to ever fly in space.
Branson's congratulatory message came nine days after he catapulted into space with five crewmates from his Virgin Galactic space-tourism company over the New Mexico desert. Branson marked history as the first person to do so in their own rocket.
And although both prominent businessmen in the space tourism industry – along with SpaceX CEO Elon Musk – have been racing to send tourists into space, all three have been supporting each other in their efforts to do so.
Before Bezos took off, Musk wished the team good luck on Twitter.
Musk also went to New Mexico earlier this month to watch Virgin Galactic's historic moment and congratulated Branson on a "beautiful flight."
Similarly, Bezos sent a congratulations message on Instagram to Branson saying, "Can’t wait to join the club!" – though he also took to Twitter a couple of days earlier to enumerate the ways in which he believes his company’s tourist rides will be better.
The Associated Press contributed to this report.