The 33-year-old, who had one year remaining on his two-year contract with the Bantams, told Press Association Sport of his interest in a move back to former employers Torquay.
But League Two rivals Aldershot have moved quickly to snare Branston on a free transfer.
Shots boss Dean Holdsworth said: "Guy gives us a wealth of experience for League Two and has a big appetite to play.
"I believe he will also be able to help the youngsters in the squad. He possesses tremendous enthusiasm and desire and is an excellent addition to the squad."
Branston added: "I have always believed in my ability. There are no flaws in my game that I can see. Managers know what they're getting with me. I am consistent and train hard every day and work to my maximum."