Hall, 27, rejoined Glasgow from Edinburgh during the summer but then tore the medial ligament in his left knee during a Scotland squad session in late July, the injury which forced him out of the World Cup.
Glasgow head coach Sean Lineen said: 'Dougie has worked hard to get back and has looked good in training. His return to fitness means competition intensifies for the hooker position where Fergus Thomson has been in fine form.'
Hall, 19-times-capped, played 11 times for Glasgow during his previous stint between 1999 and 2002, and is eager to resume.
He said: 'Picking up an injury as you move to a new club is not to be recommended when it's already going to be a hard battle to win your place in the side and that's what I'm concentrating on just now.'
Elsewhere Lineen makes two changes to the starting XV that defeated league leaders Cardiff Blues at Firhill last week.
Lome Fa'atau returns on the wing for Hefin O'Hare, while Graeme Morrison is chosen at outside centre with Andrew Henderson switching to inside centre as Daryl Gibson rests an Achilles.
Lineen said: 'Lome is a quality international player who's maybe taken a wee while to adapt to the differences between Northern and Southern Hemisphere rugby. But he has a lot to offer and is very much up for tomorrow's game.
'Graeme Morrison enjoyed his run-out against Viadana and I'm looking for him and Hendo to make their mark against Connacht.
'We've selected the same pack as started against Cardiff as Connacht will look to challenge us up front. Connacht could have beaten us at Firhill in October and they'll have targeted this game to get them back on the road after their loss to Ulster last week.'
Joining Hall as a change to the bench is his fellow front-row forward Mike Collins, with O'Hare filling the outside back slot instead of Morrison.