The England attacker also moves to Barca on-loan for the season with an option set at €30-35m. The entire loan-to-buy deal is the second richest of it's kind in LaLiga history behind only Antoine Griezmann.
Speaking to the club's media after the move was confirmed, Rashford admits he had pushed to join Barca in January.
He said, "I already tried to come this winter, but in the end it couldn't be and I went to Aston Villa.
"It's simple, I want to win everything. I think I've arrived at the best place to win everything. It's a very ambitious team. And I know that the Champions League is the big goal, the dream of all the fans.”
A number full of history
Rashford admitted he's living a dream: "I'm very clear that I wanted to come here. I want to start playing in front of my new fans and at a club where I feel at home on the first day."
Rashford will wear the No14 at Barca this new season, a number formely of Dutch great Johan Cruyff.
He also said: "I know that 14 is a historic number. I'll give my all to wear it with pride. I know the demands I have."
On Barca coach Hansi Flick, Rashford added: "He's one of the people who believed in me. I'm grateful and motivated.
"I'm here to enjoy myself and improve, and if possible, score a lot of goals."