Skysports.com understands Paul Jones will complete his permanent move to Peterborough after agreeing a one-year deal.
The 24-year-old spent the second half of last season on loan at London Road from Exeter and he clearly impressed the club's hierarchy.
Jones featured in all three of the club's League One play-off matches, including their 3-0 Old Trafford success over Huddersfield Town.
Chairman Darragh MacAnthony revealed earlier this month the club had offered the keeper a contract, a deal he has now accepted.
The free agent will put pen-to-paper on a one-year deal with Peterborough on Friday morning before joining their pre-season training.