Chelsea have paid Wigan £9m to sign the 21-year-old forward, who completed a medical on Friday evening.
Moses departs Wigan having scored nine goals in 80 appearances for the club. His final game as a Wigan player came in the weekend's defeat to his new employers.
Prior to confirming the signing of Moses, Chelsea manager Roberto Di Matteo said: "(Wigan manager) Roberto Martinez has done a wonderful job with this player since signing him. He's really developed him.
"He had a very good season last year and hopefully we can progress his development.
"He can play on either wing and will give the team width. He has good dribbling ability, has pace and is powerful.
"We've tried very hard to get this player. We like him very much. He's young and hopefully he'll be the future of the club."
Earlier on Friday, Chelsea made Marseille defender Cesar Azpilicueta their fourth summer signing as he joined Eden Hazard, Oscar and Marko Marin at Stamford Bridge. That attacking trio cost Chelsea a total of £64m, with Belgian playmaker Hazard accounting for half of that sum.
With Marseille receiving a fee of £7m for the attacking full-back, that brought Chelsea's outlay since winning the Champions League in May to £71m, with Moses making it a round £80m.