'Sky Sports' is reporting that the deal has been completed, but neither Preston nor Rangers have officially announced the signing.
Garner scored 57 goals in 151 games for Preston North End in a three-year spell at the club.
The 28-year-old started both of Preston's first two league games but was not included in the squad for the club's defeat to Derby.
Despite the imminent signing of Garner, Rangers have missed out on Aston Villa defender Joleon Lescott, who turned down a move to the Gers for 'personal reasons'.