The 28-year-old Republic of Ireland internationalist began his career at Everton and played for Blackburn Rovers before a switch to Brighton in 2016.
Celtic manager Neil Lennon told the club website: “We are delighted to bring a player of Shane’s quality to Celtic. He is an international player with so many great attributes. He is a leader and he’s a warrior – someone with real ability and who will also give us that great physical presence."
