Moses spent last season on loan at Liverpool but struggled for game time in Brendan Rodgers' title-chasing side.
Jose Mourinho who featured him for in the Blues’ pre-season win over Ferencvaros admitted he was considering keeping hold of Moses earlier this week but the Nigeria is thought to want first team football, which he is unlikely to get at Stamford Bridge with competition from the likes of Eden Hazard, Willian and Andre Schurrle.
"We are delighted to have secured the services of such an exciting young talent in Victor,” Stoke's chief executive Tony Scholes told the club's official website.
"He will certainly add to our attacking options and from talking to him it's obvious that he's really excited about the prospect of making an impact in the Premier League with Stoke City."
Moses will wear the NO. 13 jersey and could make his Potters debut against Hull next weekend alongside compatriot Osaze Odemwingie.