Wednesday have given the former Rotherham player a free transfer and he has joined The Latics until the end of the season after agreeing a severance deal at Hillsborough.
Brian Talbot has apparently been in talks with Branston for a few weeks and Peterborough boss Barry Fry will no doubt be livid that he did not get first option on the 26-year-old.
Meanwhile, Paul Sturrock has said he is not signing Plymouth pair Hasnay Aljofree and David Norris on loan despite press reports this morning.
Aljofree did a good job for The Owls in an earlier loan spell at Hillsborough but went back to Home Park early because of an injury.