The move sees the 29-year-old former Nigeria international team up again with former Blues boss Antonio Conte.
"It's an honour for me to be here and be an Inter player," Moses said on Inter TV.
"I'd like to thank everyone for the welcome I've been given, I can't wait to start."
Moses added that he is looking forward to renewing his relationship with Conte, having won the 2016-17 Premier League title together at Stamford Bridge as well as the FA Cup.
"Having the opportunity to work with the coach again is something I'm really happy about," said Moses. "I have spoken to him and he has already explained the club's project to me. I want to be part of it."