The centre-back has put pen to paper on a six-year contract running until 2032.
Lacroix becomes the latest addition to Xabi Alonso's squad this summer, joining Emmanuel Emegha, Marco Palestra, Geovany Quenda and Morgan Rogers among Chelsea's recruits, and takes the club's summer spending beyond £250 million.
He arrives already familiar with several of his new team-mates, having faced them as a Palace player over the past two seasons and spent this summer alongside Malo Gusto in France's World Cup squad, which finished fourth.
"I think it's the best move for me because it's the best club in the world," Lacroix said. "I spoke with Malo.
"I spoke with Trev [Chalobah]. I spoke with Benoit [Badiashile]. It's easy for people to speak well about this club because it has a lot of big history and I'm really proud to be a part of it now."
The defender said conversations with Alonso himself were decisive.
"I spoke with the manager on the phone. We spoke about tactics, we spoke about how he sees the game. First of all, I was happy just to speak about football with him, and I saw that we have the same direction and desire for this club," he said, adding that team-mates who know Chelsea from the inside reinforced the decision.
"When I spoke with the gaffer, when I spoke also with the people I know from the national team who play for Chelsea, like Malo, they told me it was the best club I can go to. So already I was saying: 'Okay, I don't need to think too much.'"
Lacroix made 98 appearances for Palace across two seasons at Selhurst Park, winning the FA Cup, UEFA Conference League and Community Shield, and had become a vice-captain at the club following Marc Guehi's departure to Manchester City in January.
Recalling his previous visit to Stamford Bridge, Lacroix added: "I have only played once at Stamford Bridge but I remember the day very well. We drew and it was an unbelievable day. To be honest, it felt good playing there. So now I'm just waiting to take my first step there as a Chelsea player."