The 29-year-old has been in fine form since arriving on a short-term contract back in September, scoring five goals for Gareth Ainsworth's side, and has now been rewarded with a new deal.
"I feel like I've done alright in the time I've been here and want to continue and help us move up the league," Morgan told the club's official website.
"I'm enjoying myself, enjoying playing under Gaz and he gives me the freedom to play my game. I love all the boys too.
"It was a no-brainer - I'm 40 minutes from home and closer to my family and friends. When you've got a circle like that, you don't want to break it."
The Chairboys are the 12th club of a career that has seen Morgan play for the likes of Colchester, Luton, Chesterfield and Oxford.