The 26-year-old France international has signed a six-year contract that will keep him at Stamford Bridge until 2032 as Chelsea continue to strengthen their squad ahead of the new season.
Lacroix said he was proud to join one of England's biggest clubs and is determined to help Chelsea compete for major honours.
"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," he said.
"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 arrives after an impressive spell at Crystal Palace, where he established himself as one of the club's key defenders. He made 55 appearances in all competitions last season and played an important role in Palace's UEFA Conference League triumph, the first European trophy in the club's history.
He also featured in Palace's Community Shield victory over Liverpool and earned a place in France's 2026 FIFA World Cup squad, making three appearances during the tournament, including a start against England in the third-place play-off.
The centre-back joined Palace from Bundesliga club Wolfsburg in August 2024 and went on to make 98 appearances across two seasons before securing his move to Chelsea.
Chelsea play Tottenham Hotspur next in a pre-season club friendly on Saturday at the Accor Stadium in Sydney, Australia.
Jack Grealish has dismissed suggestions that he was dropped from Manchester City's pre-season tour, insisting he is still recovering from injury rather than being left out by head coach Enzo Maresca.
Newcastle United have decided to amicably part ways with manager Eddie Howe just a few weeks ahead of the upcoming 2026/27 campaign.
Tottenham manager Roberto De Zerbi has made it clear he wants Lucas Bergvall to remain at the club, but insists no player can expect an automatic place in his starting line-up.
Liverpool maintained their winning start under new head coach Andoni Iraola after teenage forward Rio Ngumoha scored the only goal in a 1-0 pre-season victory over Wrexham at New York's Yankee Stadium on Wednesday.
