The France centre-back, 26, moves across London to Stamford Bridge, penning a six-year contract until 2032.
Lacroix was a regular fixture in the Palace team last season, making 55 appearances across all competitions.
He helped Palace win the Conference League – the club's first-ever European trophy – and played in their Community Shield victory over Liverpool.
"I am really happy to be part of this beautiful club. Everyone knows the legend of Chelsea, its tradition of winning, and to be a part of that is a proud moment," said Lacroix.
"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."
Lacroix earned a place in France's World Cup squad and made three appearances, including a start against England in their third-place play-off defeat.
Palace signed Lacroix from Bundesliga side Wolfsburg in August 2024 and he played 98 times in two seasons for the Eagles.