Arsenal striker Lukas Podolski is in talks over a move to Galatasaray, according to Sky sources.
England goalkeeper Tom Heaton has committed his future to Burnley by signing a new contract until June 2018.
Stoke announced a deal for the 23-year-old forward had been completed on their official Twitter account.
Moses has struggled to make an impact at Stamford Bridge since moving from Wigan in 2012 and spent last season on loan at Liverpool, but he started just six Premier League matches for the Merseysiders, scoring two goals.
Stoke have been trying to add some natural width to their team and have spent much of the summer pursuing a deal for Liverpool’s Oussama Assaidi, who spent last season on loan at the Britannia Stadium.
Manager Mark Hughes admitted his interest in signing Nathan Redmond from Norwich City earlier this week but seems now to have opted for a move for Moses.
"We are delighted to have secured the services of such an exciting young talent in Victor," Stoke's chief executive Tony Scholes said on the club's 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."