Flankers Scott Newlands and Ross Rennie also come in, the latter following reconstructive knee surgery, and Chris Paterson takes the captain's armband following Roddy Grant's injury.
But with certain sections of the home support unhappy with Godman's displays last season, Moffat has tipped the stand-off to take a leaf out of Dan Parks' book and silence the boo boys.
He said: "Phil can kick on again and do what Dan has done.
"Two years ago you would not have thought Dan would be playing like he is just now.
"Against us Dan never made a mistake in giving Cardiff direction. You need one or two boys on the pitch who know how to do the right thing at the right time.
"At 28 Phil is approaching his peak but there are players at Edinburgh still improving in their 30s and he can do the same by getting better and better."
Meanwhile Glasgow head coach Sean Lineen makes two changes to the team that registered a pulsating 22-19 win over Leinster.
Ed Kalman replaces Moray Low at tighthead prop, while Canadian international Chauncey O'Toole will make his debut at blindside flanker after signing this week in place of Ryan Wilson.