The former Barca youth rejoined the club from Valencia in the summer and has said that he hopes the "dream" of playing for them can continue.
"It was a dream to come back and I'm playing at a good level," Alba told the club's official website. "It feels like I've been here for years. I hope to stay a very long time.
"I'm at the best club in the world and I play for the team that plays the best football. I'm very content, I can't ask for more."
Alba has scored twice in 18 league games for Barca.