Under the terms of his contract with the south coast club, which only had a year to run, the Frenchman will not cost the Whites a bean.
The midfielder joined the Seagulls last summer on a free from Monaco but a clause inserted in his contract also allowed him to leave for free if the club were relegated.
Brighton chairman Dick Knight told the Brighton Evening Argus: "If that clause hadn't gone in then Seb's wages over the two years would have been higher and the signing-on fee would have been more, so it was a no-brainer.
"If we'd had to buy him on the open market he would have cost around £350k. West Ham had offered 600,000 Euros to buy him a few months before we signed him.
"We fought hard to keep him but the agent has persuaded Seb to go."
Brighton boss Mark McGhee also admitted his disappointment that Carole has decided to move on.
He said: "I am very disappointed. We gave Seb the opportunity to come here and be part of the team. Regardless of that clause the decent thing for him to do would have been to stay, at least at the start of the season.
"I think he's a player that would have been a major help in us getting out of this division."