Experienced frontman Fagan, who counts the likes of Birmingham, Derby and Hull among his former clubs, has signed a permanent contract until the end of the season.
He was most recently at Bradford last season, making 35 appearances and finding the net eight times before being released.
Clarke-Harris, meanwhile, has arrived on loan from Championship side Peterborough until the end of the campaign. It comes after he spent a month with Southend earlier this season.
Both players go straight into the Shakers squad to face Coventry at Gigg Lane this weekend.