The 18-year-old goalkeeper was at the Hoops for the last 10 years and was in the development squad behind Ross Doohan and Conor Hazard.
Despite his talent, he was never close to reaching the first team due to the high level of competition for places at Parkhead.
McAdams represented Scotland in the U17 European Championships finals last summer in Azerbaijan, where they finished bottom of their group.
The youngster attracted late interest from several English clubs, however Celtic reached an agreement with Rangers.
The Hoops have profited from their fierce rivals for a player that was not going to be a key aspect of Brendan Rodgers’ squad, as they strive to create even more history next season.
Celtic’s job of developing the keeper is complete, and they strive to continue bringing through youth talent who have the ability to break into the first-team.
The youngster is thought to have signed a three-year-contract with the Ibrox club.