The 23-year-old winger becomes the Potters' sixth signing ahead of the 2014/15 Barclays Premier League campaign, which gets underway this afternoon with the visit of Aston Villa to the Britannia Stadium.
Moses is not eligible for the clash with Villa but Bojan, Mame Diouf, Phil Bardsley, Steve Sidwell and Dionantan Teixeira could make their debuts for the Club.
City Chief Executive Tony Scholes said: "We are delighted to have secured the services of such an exciting young talent in Victor.
"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."
A Nigerian international, Moses started his career with Crystal Palace but got his first taste of Premier League action with Wigan following a £2.5million move to the North West in January 2010.
He joined Chelsea in the summer of 2012 and has made 23 league appearances for the West London outfit and 19 for Liverpool while on loan at Anfield last season.