The Scotland international, who won first cap against the Faroe Islands in 2010, agreed to be registered with effect from September 1.
He consequently joined the first-team squad for the start of pre-season training at Murray Park in June.
Bell played 33 times for Kilmarnock in the season before arriving at Ibrox and had been contracted to the Ayrshire side for the last decade.
He made his debut for them in May 2009 after playing 16 games on loan at Queen of the South.
He then made another 130 appearances for the Rugby Park outfit and was widely linked with a move to Ibrox for several months before his move.