The 28-year-old Welsh international has re-joined the Seagulls on a three-year deal after two seasons away, in which he won promotion to the top-flight with Norwich City
Crofts has signed a three year deal to join up with manager Gus Poyet, who made the player his "number one midfield target".
"When we knew about the possibility to bring him back we worked very hard to do that, and it took a few weeks, but we are very pleased to have him," Poyet told the club's official website.
"We respected his career and helped him when there was interest from Norwich two years ago, and he went on to become a very good Championship player, as well as proving himself in the Premier League."
Poyet also explained how he chose Crofts because of the experience of playing in the Premier League, where Poyet believes he gave a good account of himself.
He added: "Now I am delighted to have him back and he is going to be a very important player for us. We were always looking to bring experienced players who know this division and the Premiership, and 'Crofty' has all of that.
"He is coming back to a club that he knows and he was happy to come back - that shows his commitment. I know how much he cares about winning football games. He leads by example and we want players like that on the pitch."
Crofts made 44 appearances in the 2010/2011 season in which Norwich won promotion to the Premier League after moving from Brighton.