Frenchman Vincelot, 27, joined the Seagulls in 2011, and he played 20 times for them last season, scoring once.
But this season he had been surplus to requirements and spent the first half of the season on loan at Gillingham.
Albion boss Gus Poyet told te club's website: "We thank Romain for his contribution to the club throughout his time at Brighton.
"He helped the side in many different positions last year but with the players we brought in over the summer he knew that his chances would be limited this season.
"We were honest with him and he was a great professional around the club and on the training ground.
"We wish him all the best of luck for the rest of his career."
Former Liverpool trainee McGiveron joined the club on a development contract last summer but he has failed to make the breakthrough and both he and Vincelot are free to find another club.