The midfielder, who was linked with a move to Liverpool, has been signed for a deal worth £58 million ($69.96 million), according to British media.
Lavia signed for Manchester City at 16 in 2020 but made just two appearances before joining Saints in July 2022 for 10.5 million pounds.
"I'm really happy to 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," Lavia said.
"I can't wait to meet all my new teammates and build a chemistry together to achieve great things together."
Lavia made 34 appearances in all competitions for Saints, scoring once, but was unable to prevent Southampton's relegation from the Premier League.
"He demonstrated his quality in the Premier League last season at Southampton, showing maturity despite his young age...," Chelsea's co-sporting directors, Laurence Stewart and Paul Winstanley, said in a joint statement.
"We believe he is ready to make an impact at Chelsea throughout the current campaign and in the coming years."
