Experienced McMahon previously held the role of assistant manager at fellow National League side Morecambe and joins Robbie Savage's backroom staff.
He spent a number of years at Tranmere Rovers including two stints as caretaker manager.
More recently, McMahon was number two to current Shrimpers boss Derek Adams in a couple of spells in the north west.
During his time with the club, McMahon helped guide them to promotion from League Two through the play-offs in 2021.