Ms Funk and Mr Daemen are the oldest and youngest people to fly into space, respectively.
The flight lasted around 11 minutes from launch to capsule landing.
Astronauts experienced three to four minutes of zero-gravity and travelled above the Karman Line, which is considered to be the boundary of space.
After the launch, the group of four could be heard cheering as they reached the edge of space before the cabin carrying Mr Bezos and his crewmates landed successfully back on earth.
Shortly after the soft landing, a voice that appeared to be that of Mr Bezos could be heard saying: “Best day ever.”
When asked by mission control how he was, his brother Mark said: “I am unbelievably good.”
As the four adventurers exited the cabin, they were greeted with cheers and champagne from family and friends, with the Amazon founder seen hugging his parents Jackie and Mike as he exited the cabin.
The trip is the 16th lift-off made by New Shepard and its first to carry human passengers.
Ahead of the flight, the 57-year-old said he was “not really nervous” and “excited” for his flight to the edge of space.
“This vehicle’s ready, this crew’s ready, this team is amazing, we just feel really good about it,” he told CBS This Morning.
Eighty-two-year-old Ms Funk, who is the oldest person to ever venture into space, said she felt like she was 24: “It’s great, I love being here.”
After the flight, the crew were each presented with a pin in the shape of the letter A, made up of the road to space representing the two side arms, and a feather - Blue Origin's symbol - making up the cross bar.
The point of the A was topped with a small blue sapphire as a symbol of Earth.
Before describing the experience Mr Bezos 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."
Referring to how the flight felt, 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 commented on seeing the atmosphere of Earth and how fragile it looked.
The journey follows Sir Richard Branson’s recent successful Virgin Galactic voyage on July 11, an experience he described as “more extreme than I’d have ever imagined”.
Blue Origin is planning two more flights before the end of the year.