The plane, with a wing span of three feet and made of paper straws, was launched using just a large helium balloon.
The craft soared to 90,000 feet before the balloon exploded, after which the plane glided back to the ground, taking photographs as it descended.
Named Operation PARIS (Paper Aircraft Released Into Space), the project cost £8,000, reports the Daily Mail.
It was the work of space enthusiasts Steve Daniels, John Oates and Lester Haines, who said they came up with the idea after being inspired by an equally ingenious project — of sending a lump of cheese into space.
The team launched the balloon from a remote spot around 50 miles west of Madrid. It took an hour and a half to climb to 90,000 feet, before bursting.
The team tracked the plane using a GPS navigation system as it took another 90 minutes to glide back to earth and landed in woodland 100 miles from the release point. But for a hole in a wing, their creation was undamaged.
Software consultant Daniels, 42, of Paignton, Devon, said the team had embarked on the project “for a laugh”. Although they spent around £8,000 to make it a success, he said he would happily do it all again.
The married father of two added: “Somebody launched a bit of cheese out of a balloon, which we thought was a bit stupid. We thought we could do something more technical than that.
First time
“We decided to launch a paper plane because nobody has done that before. It seems really silly but it was brilliant fun.”
He told Sky News Online: “We did it because we wanted to see if we could — and we could!
“We expected a few niggles and thought that the plane would come back to earth in bits but it was all in one piece.
“It’s a world first, I believe. I understand the Australians are going to challenge us and we look forward to that. But we did it first!”
The three enthusiasts got together after discussing the project on tech website The Register.
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