The 23-year-old former Crystal Palace and Wigan Athletic player, who was on loan at Liverpool last season, is Stoke's sixth new recruit of the summer.
"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."
Moses, a Nigeria international, will play no part in Stoke's season opener against Aston Villa later on Saturday.
Stoke have been busy in the transfer window as they try and build their ninth-placed finish last season.
Bojan, Mame Diouf, Phil Bardsley, Steve Sidwell and Dionantan Teixeira were all in line to make their debuts against Villa at the Brittania Stadium.