The Nigeria international will spend the rest of the season with Mark Hughes's side after completing a temporary move to the Britannia Stadium.
The 23-year-old, who joined Chelsea from Wigan Athletic in Aug. 2012, has endured a largely unsuccessful spell at Stamford Bridge, failing to establish himself as a first-team regular with the London club.
The Nigeria international spent last season on loan at Liverpool, but managed to score just two goals in 22 appearances as the Merseyside club narrowly missed out on the Premier League title with a second-place finish.
MORE: Coach Ted Lasso returns! | Porter challenges Guardiola | WAGs
He will hope to make more of an impression with Stoke, which is looking to continue its progression after recording its highest Premier League finish of ninth in the 2013-14 campaign.
Stoke's chief executive Tony Scholes told the club's official website: "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."
Moses' arrival bolsters Mark Hughes' side further following the signings of Mame Biram Diouf, Phil Bardsley, Steve Sidwell, Bojan Krkic and Dionatan Teixeira.