The 22-year-old joined Torquay on non contract terms in November, making 13 appearances for the Conference club, having left Plymouth in the summer.
But he departed Plainmoor last week after the club were unable to offer him a permanent deal owing to financial constraints.
Derby-born Berry was at Aston Villa as a youth player, having started out on the books of Notts County. His father Dennis was a professional boxer in the 1990s.
Berry becomes boss Paul Buckle's first permanent signing as Cheltenham boss and he will go straight into the squad for Saturday's trip to Dagenham and Redbridge.