The Belgium Under-21 international has joined Saints on a five-year contract.
According to various reports, the transfer for Lavia saw Saints pay City an initial £10.5m with a further £3.5m in add-ons on top of a 20% sell-on clause.
Manchester City also have a buy-back option for the 18-year-old central midfielder, said to be worth around the £40m mark.
Lavia joined City from Belgian side Anderlecht at 16 after eight years at the club.
Despite his age, Lavia featured for Pep Guardiola’s City first team in both the Emirates FA Cup and Carabao Cup last season.
The Belgian is said to be an energetic ball-winning midfielder who could well be what Saints’ midfield needs.
Southampton manager Ralph Hasenhuttl is hoping Lavia can hit the ground running at Saints and prove why he should be a Premier League regular at St Mary’s.
“Roméo is an extremely talented young player at the start of his career who is open-minded and wants to learn and develop his game with us,” Hasenhuttl said in the official press release.
“We are very excited to sign him ahead of many other interested clubs. It proves that we have a positive reputation for improving young players, which we have worked hard to build up over the years.
“Roméo is coming from one of the best teams in the world, learning from the best manager and the best players. Now it is up to him to show us why he deserves to play in the Premier League, as we hope to help take his game to the next level.”
As Hasenhuttl hinted, Southampton’s reputation as a place for young players to shine and be given first team opportunities is what attracted Lavia to the South Coast.
“I’m really delighted to join this club. I think this club has a really good culture with young players, so I’m really happy to be here,” Lavia said.
“When I heard of the interest of Southampton I was buzzing because there’s an opportunity for young players to develop as much as possible and I’m very excited.”
Lavia is Southampton’s fourth signing of the summer transfer window, following the arrivals of Gavin Bazunu - also from Man City - Mateusz Lis and Armel Bella-Kotchap.