The 23-year-old, who joined Barca in 2007, has signed a three-year deal at the Balaidos.
Fontas struggled to make an impact at Camp Nou after an anterior cruciate knee ligament injury suffered in January 2012.
However, his impressive spell on loan at Mallorca earned him a move to Celta Vigo, where he will team up with former Barcelona B coach Luis Enrique.
"I chose Celta because of the project," Fonast told reporters after his move.
"I like the way the team plays and the forward-thinking mentality of Luis Enrique."
Fontas made 16 appearances in his time at Barcelona, scoring one goal.