The British businessman was technically the winner of the so-called “billionaire space race” as he won the battle to be the first to launch himself into space.
However, Bezos on Tuesday went further - reaching 66 miles compared to Branson’s 53.
“Well done @blueorigin, @jeffbezos, Mark, Wally and Oliver. Impressive!” Branson wrote.
“Very best to all the crew from me and all the team at @virgingalactic.”
Bezos blasted off in the sub-orbital New Shepard rocket from Texas on Tuesday, the 52nd anniversary of the Apollo 11 moon landing.
Minutes later he emerged safely from the capsule after it landed softly on the ground, slowed down by three huge parachutes.
He took off with his brother Mark, female astronaut Wally Funk, 82, who trained in 1961 but never went to space, and the company’s first customer, Dutch 18-year-old Oliver Daemen.
Ms Funk and Mr Daemen are the oldest and youngest people to fly into space respectively.
She took on board a postcard of herself standing in front of the American flag, having promised to take a picture with it and Earth in the background.
The crew members also took a number of historic items with them, including the goggles Amelia Earhart used to fly across the Atlantic and a brass medal made from the first hot air balloon which flew in 1783 – the first time humans left Earth in control of flight.
The crew also carried a piece of canvas from the Wright Flyer – the plane flown by the Wright brothers.
During a post-flight press conference Jeff Bezos presented his mother with a feather necklace he wore on the flight.
Speaking at the event, he thanked all the engineers at Blue Origin, saying the crew owed them a “deep gratitude”.
He also thanked every Amazon employee and customer, saying “you guys paid for all of this”.
He added: “Thank you from the bottom of my heart, very much. It’s very appreciated.”
Speaking about the flight, Mr Bezos said: “Oh my God. My expectations were high, and they were dramatically exceeded.
“The zero Gs may have been one of the biggest surprises, because it felt so normal.
“It felt like, almost like we were as humans evolved to be in that environment, which I know is impossible, but it felt so serene and peaceful and the floating.
“It’s actually much nicer than being in full one gravity.”
He said how fragile the atmosphere of Earth looked, adding: “We are damaging it.”
“This is the only good one, I promise you, and we have to take care of it.
“And when you go into space and see how fragile it is you’ll want to take care of it even more.”