Southampton sign Argentine midfielder Carlos Alcaraz for £12m
The 20-year-old midfielder is the second most expensive sale in Racing's history, after the 25 million euro (£22m) Inter Milan paid for Lautaro Martinez in 2018.
He has signed a four-and-a-half year contract.
The fee includes a 15 percent sell-on clause.
"I don't know if this is the time to go or not, it was decided by the clubs," Alcaraz told TyC Sports in Argentina before leaving for Britain to take a medical and sign his contract.
"I know I'm going to miss Racing a lot because it's my home, every day and also the fans because of what they make you feel."
He played 83 times for Racing, scoring 13 goals and providing six assists.
Southampton are currently rock bottom of the Premier League following a dire run of six straight defeats in the league.
They sacked Austrian manager Ralph Hasenhuettl in November at the beginning of that run but his successor Nathan Jones has been unable to stop the rot.
