The 32-year-old Republic of Ireland international successfully passed a medical on Friday before sealing the move.
"We are pleased to welcome Keith to the club," manager Oscar Garcia told Brighton's official website. "He is a player with experience at the top level of the English game and international football – including World Cups and European Championships.
"Keith is a player who I know will enjoy the way we like to play. He is a dynamic and energetic player and brings different qualities which will complement our existing midfielders, and he will bring added competition to our midfield."
Andrews joined Bolton from West Bromwich Albion last summer.