Chelsea’s hunt for a new first team centre appears to be over with Lacroix, 26, joining for a reported £52 million from Crystal Palace.
It was widely reported that it was a priority position for new manager Xabi Alonso, although it remains to be seen what kind of system the Spaniard will be playing.
The France international heads to Stamford Bridge on a deal that will keep him there until 2032, becoming Chelsea’s sixth addition of the summer.
"I am really happy to be part of this beautiful club," Lacroix told the club’s website. "Everyone knows the legend of Chelsea, its tradition of winning, and to be a part of that is a proud moment.
"When I spoke with the manager, I saw that we have the same direction and desire for this club. We want to win.
“When you see the quality of the players here, everything we have around the club, it's something that we can achieve. The ambition is to lift trophies, and I can’t wait to contribute."