He said: "To make the step up to the Premiership now is a dream come true. I'm massively excited about joining Warriors and it's a fantastic opportunity.
"It's taken a while to get this first Premiership contract and I'm really happy. I can't wait to get involved and get my hands dirty."
Stephenson, who was born in Kent, has scored 15 tries in 17 matches for Bedford this season and has helped his current club to third position in the table.
He has proved to be one of the most dangerous wingers in the RFU Championship and says he will now be aiming to help Warriors rack-up the tries.
He continued: "I want to continue running the ball as much as possible. The strength and conditioning side of things here will help me get better and become more elusive.
"I like scoring and try to pop up in the right place at the right time. If I don't score, it's not everything. I like to put my body on the line as well and put myself out there."
With Bedford still chasing promotion to the Premiership after 12 wins from 19 games, Stephenson insists he is still focused on helping his current side finish as strongly as possible before moving to Sixways.
He added: "I've loved it at Bedford and I'm so grateful for the opportunity they gave me. They play a great brand of rugby and without that it wouldn't have been easy to get noticed.
"I'm looking forward to finishing the season with them and hopefully we can get quite a few wins under our belt and make some memories."