Firpo, 24, has agreed a four-year deal at Elland Road and will join up with Marcelo Bielsa's squad for preseason immediately.
AC Milan also held talks with Barca about a loan move, but the Catalan club always made it clear they would prioritise a permanent transfer.
Leeds emerged on the scene at the end of May and director of football Victor Orta played a key role in selling the club to Firpo.
The former Spain Under-21 international wanted to leave Barca in search of regular football and was convinced he would be the perfect fit in coach Bielsa's system.
✍️ #LUFC is delighted to announce the signing of Junior Firpo from Barcelona— Leeds United (@LUFC) July 6, 2021
For Barca, the deal represents a much-needed injection of cash as they look to reduce their debt and bring their wage bill under control.
Barca are finding it harder to move on some of their bigger earners, with Neto, Samuel Umtiti, Miralem Pjanic, Philippe Coutinho and Martin Braithwaite among the other players made available for transfers this summer.
After moving to Spain from the Dominican Republic at the age of six, Firpo joined Real Betis as an 18-year-old in 2014.
He went on to make 43 appearances for Betis' first team before Barca signed him as competition for Jordi Alba for an initial €18m in 2019.
However, first-team opportunities have been hard to come by at Camp Nou, where he has been restricted to just 22 starts across two seasons.