Moses had been on loan at Turkish side Fenerbahce but heads to the San Siro in a move that will see him reunited with former Chelsea boss Antonio Conte.
"Having the opportunity to work with the coach again is something I'm really happy about. I've spoken to him, and he's already explained the club's project to me. I want to be part of it, I'm happy to be here. I'll give my all and want to help the team. There's a lot of quality here, I want to make my contribution out on the pitch and enjoy myself. That's the most important thing."
Conte successfully converted Moses from a winger to a wing-back during his two years at Stamford Bridge, and the Nigerian played a key role in the Blues' Premier League title win in 2017:
Squawka Football @Squawka
Victor Moses' 2016/17 Premier League season by numbers: 34 games played 28 games won 172 recoveries 120 crosses 54 take-ons completed 47 tackles made 41 interceptions 32 fouls won 28 chances created 3 goals 2 assists 1 title Reunited with Antonio Conte. 🏆 https://t.co/IJ6iLRmFkq
Moses and Conte also won the 2018 FA Cup at Chelsea with a 1-0 win over Manchester United, but the Italian was sacked two months later by the Blues and replaced by Maurizio Sarri.
The arrival of Sarri saw Moses fall out of favour at Chelsea, and he left to join Fenerbahce on an 18-month loan in January 2019:
Moses made 16 appearances for Fenerbahce in his first season with the club but has only featured six times in 2019-20 and has been sidelined since November because of injury.
He will now be hoping to kickstart his career with a coach he knows well and enjoyed success with during their time in the Premier League.
Moses becomes Inter Milan's second recruit of the January transfer window and follows Manchester United's Ashley Young in making the move to the San Siro.
Inter chief executive officer Beppe Marotta told football journalist Fabrizio Romano the club are also in talks with Tottenham Hotspur over a move for Christian Eriksen and will also make a decision on whether to sign Chelsea striker Olivier Giroud.