The Blues struck a £58million to sign the highly-rated midfielder, taking the club's total spend under Todd Boehly close to £1billion.
Liverpool had agreed a £60m deal for Lavia but, for the second time this week, the Reds were pipped to the line by Chelsea following Moises Caicedo's British-record switch.
Taking to Instagram, Lavia wrote: "To Saints Fans. As I say goodbye, I want to say a big thank you for everything you have given me during my time here.
"I've instantly felt the love from you all despite us not achieving our shared goals. I'll never forget the belief the club and Saints all around the world showed me and I hope I was able to repay the faith you put in me.
"I would especially like to thank all my teammates and all staff members within the club involved closely or not for putting your arms around me since the day I walked through the Staplewood Campus and for all the daily work and help behind the scenes making me become a better person, athlete and football player.
Read more on Chelsea
Jordan reveals how Chelsea can fund deals for Caicedo and Lavia and NOT breach FFP rules
Kepa Arrizabalaga completes loan move to Real Madrid from Chelsea
"You have all played a massive part into making my integration into real professional football easier. I will be forever grateful to you. For those reasons, this club will always remain close to my heart.
"Good luck this season and I look forward to seeing the club marching back to the Premier League where it belongs very soon! Thank you Saints. Roméo."
The signing provides boss Mauricio Pochettino with another option as his midfield reconstruction continues to take shape.
Lavia will compete with Caicedo, Enzo Fernandez, Conor Gallagher, Carney Chukwuemeka and Lesley Ugochukwu for a starting spot.
Most read in Football
Lavia leaves Southampton for Chelsea, Everton move for Adams, Liverpool to seal Endo deal
Former Arsenal star Walcott announces retirement and thanks two managers in farewell video
Crystal Palace brutally troll Chelsea with hilarious song choice on Michael Olise video
TV star Rachel Riley says she won't support ManUnited if Mason Greenwood returns to action
The youngster impressed during his solitary season at St Mary's and despite suffering relegation, the Belgian put himself in the shop window with a host of impressive displays.
Lavia left Anderlecht at the age of 16 to join Manchester City, signing his first professional contract with Pep Guardiola's side.
After impressing at under-18 level, Lavia was promoted to City's U23s squad and played a key role in landing the Premier League 2 title in 2021.
The teenager secured a switch to Southampton last summer but was unable to prevent the Saints from going down.
His displays earned him a call up to the Belgium squad in March for the Euro 2024 qualifiers against Sweden and Germany.