The Blues have paid an initial £53m fee to bring in the Belgium international on a seven-year contract.
Lavia came through the Anderlecht academy before joining Manchester City in 2020.
The 19-year-old left Pep Guardiola's side to join Southampton last summer and made 34 appearances across all competitions but could not prevent their relegation to the championship.
Earlier this week, Chelsea saw off the challenge of Liverpool to sign Moises Caicedo from Brighton and Hove Albion.
Lavia is Chelsea's ninth signing this summer.
On completing his move to Chelsea, Lavia said: "I'm really happy join Chelsea and be a part of this exciting project. It's an amazing football club with a great history and I'm really excited to get started.
"I can't wait to meet all my new team-mates and build a chemistry together to achieve great things together."
Chelsea co-sporting directors Laurence Stewart and Paul Winstanley added: "We are very pleased to welcome Romeo to Chelsea. He demonstrated his quality in the Premier League last season at Southampton, showing maturity despite his young age, and is a player we have monitored for some time.
"We believe he is ready to make an impact at Chelsea throughout the current campaign, and in the coming years."
Lavia could make his debut against West Ham United this weekend.
