The 24-year-old has reportedly cost the Premier League club £12.8million (€15m) just two years after he joined Barcelona from Real Betis.
Firpo had scored three goals and provided five assists from 26 chances created in all competitions in his final season at Betis, appearing 29 times.
But he struggled for opportunities at Camp Nou, with Spain international Jordi Alba the clear first choice.
Firpo scored twice and supplied two assists across two seasons for the Blaugrana, with only 22 of his 41 outings coming from the start.
He hailed Leeds boss Marcelo Bielsa as a key factor in his decision to join the club.
“I saw him [Bielsa] in Spain when he trained there,” Firpo told Leeds’ official website.
“I know the coach that he is, and for me he is a really good coach. He wants to press all the time, play one against one many times, and for me that’s my football.
“Physical football, running, having the ball, for me it’s not a problem and I think he will help me go to another level.
Firpo created 1.01 chances per 90 minutes, just shy of Alioski’s 1.02.