Alcacer, 23, was omitted from the Valencia side that lost 1-0 to Eibar on Saturday and underwent a medical at Barca on Monday before completing a move worth an initial €30million.
Barca could pay €2m more in add-on fees and have inserted a €100m buy-out clause into Alcacer’s deal at Camp Nou.
The La Liga champions’ sixth signing of the season, Alcacer concludes Barca’s long search for attacking reinforcements to support Lionel Messi, Luis Suarez and Neymar.
“When I found out about the offer from FC Barcelona I asked the club to listen to it, as it was my decision to take a step forward in my career,” Alcacer told Valencia’s official website.
“I want to thank Valencia CF and the fans. Despite the fact that I am leaving Valencia CF, I will always be a Valencianista at heart.”
Alcacer scored 43 goals in 124 appearances for Valencia and has won 13 caps for his country.