The 25-year-old spent two separate loan spells with the Bucks last term but despite top scoring with eight goals in 28 games was unable to prevent relegation from step two.
Gibson, who has previously enjoyed prolific spells with Halesowen Town, Stourbridge and Ilkeston, is a marquee signing for Bucks boss Kevin Wilkin, whose recruitment drive for the Southern League Premier Central has started in earnest.
He becomes the fourth new recruit of the summer from Wilkin in what is a complete rebuild following relegation. Gibson follows goalkeeper Brandon Hall, full-back Nathan Fox and central defender Orrin Pendley through the door at the New Bucks Head.
The former Notts County youngster’s 31-goal haul for Halesowen in 2019/20 earned him a Football League return with Grimsby Town.
Telford have also retained a few of last season’s squad, of which the only remaining contracted squad member was defender Harry Flowers.
Defenders Jordan Piggott and Brad Bood have re-signed, as has winger Byron Moore.
Former midfielder Prince Ekpolo has rejoined his old club Guiseley and wideman Adam Livingstone has left the Bucks to join Hereford. Robbie Evans and Jason Oswell have joined Newtown.