Edwards, 21, spent time on loan at the Broadfield Stadium last season and has agreed a two-year deal with the club.
Manager John Gregory told the official club website: "We all know what Gwion can give us, but I think there is a lot more to come from him.
"He's at a great age to develop his game and really move his career forward and I'm sure our supporters will be as pleased as I am that we have him now for the next two years."
Edwards scored two goals in six appearances for Crawley last season during his loan spell and has represented Wales at Under-21 level.
He has become the 10th signing of the summer for Crawley.