The 24-year-old has signed a four-year deal with the Elland Road club following successful completion of a medical and a period of quarantine following his arrival in Yorkshire.
Reports suggest that Firpo has joined for a €15m fee plus add-ons.
In a statement, Barcelona said they will retain 20 per cent sell-on of any future sale of the player.
Firpo - also linked with AC Milan - will provide a much-needed specialised option at left-back following the recent departure of North Macedonian international Gjanni Alioski - who recently left the club.
Firpo’s versatility has seen him feature at left-back, right-back and as part of a back three, but the player failed to dislodge Jordi Alba from the starting line-up at the Camp Nou last term and played just seven times in La Liga last season.
Barca, whose gross debt is over €1 billion, need to bring in money this summer to help fund arrivals and also need to reduce the wage bill to be able to register new players within the league-imposed salary cap.
Along with Neto, Samuel Umtiti, Miralem Pjanic, Philippe Coutinho and Martin Braithwaite, Firpo was one of the players who have been made available for a transfer.
Born in the Dominican Republic, Firpo has featured 41 times for Barca in the past two seasons, having made his breakthrough with Real Betis after moving to Spain at a young age.
Firpo excelled at Betis in 2018-19 - scoring three goals and contributing five assists in 29 appearances for the club with his exploits earning him a call-up to the Spanish under-19 side, where he helped them win the 2019 UEFA European Under-21 Championship.
After the tournament, Firpo secured a move to Barca on a five-year deal.
The player has become the club’s third signing of the close season following the earlier additions of Jack Harrison and Amari Miller and will wear the number three shirt at Leeds.