The 23-year-old moved to Bedford from Blackheath in 2012 after scoring 19 tries in one season in National League One.
Stephenson becomes the eighth new addition to the Warriors squad for next season and joins Ignacio Mieres, Leonardo Senatore, Agustin Creevy, Paul Warwick, Ofa Fanga'anuku, Mike Williams and Paul Andrew in agreeing contracts at Sixways.
"We are trying to build for the future and James is a real talent who is hungry and the right age," said Head Coach Richard Hill. "This year in the RFU Championship he has shown what an excellent player he is and Paul Hull has watched him closely.
"James is a player with huge potential to get even better and he has shown his undoubted try scoring ability at Bedford Blues. He is fast and he's very powerful, and being an ex-back row forward he likes the contact so is an aggressive and strong winger.
"I have always liked the way Bedford play, a real 15-man game. James has relished that approach and we need to bring players like that to Warriors, those that will fit the style we want to play.
"James has just completed his education and degree, to stand him in good stead for the future, but now is the right time for him to show his ambition and concentrate full-time on his rugby career."
Stephenson added: "I'm really looking forward to joining the club and I can't wait to meet all the boys come pre-season. Richard Hill is a great coach so hopefully I will learn a lot from him and continue my progression.
"The facilities here are better than anything I've ever seen before and the city is lovely. I've had a little look around and it seems really pleasant and relaxed.
"It's the first time I've been to Worcester and I'm really impressed. It's a lovely place and this club is the heartbeat of the city so everything is perfect at the moment."
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