During his time at Burton, Branston picked up six yellow and two red cards, leading to three separate suspensions.
The defender, who has also had lengthy spells with Oldham and Rotherham, played seven times for Plymouth Argyle on loan in the 1998-9 season.
Speaking before Torquay's recent 3-2 defeat by Burton, manager Paul Buckle admitted to BBC Radio Devon that Branston was a player the Gulls had been chasing during the close season last summer.
Buckle said: "We was looking at Guy Branston, but we decided against that one in the end.
"So we're more than pleased with Kieran Charnock, [Chris] Robertson and [Mark] Ellis at the moment."
Branston is expected to go straight into Torquay's squad for the Saturday's fixture with Bradford City at Plainmoor.
Source: BBC Sport