The 26-year-old centre-back is set to undergo his medical with Chelsea before signing a bumper six-year-deal until the summer of 2032, as per David Ornstein of The Athletic.
Lacroix made 55 appearances for Palace last season, scoring three times and providing three assists.
His strong performances earned him a place in France's World Cup 2026 squad, where he made three appearances.
The French international has been viewed as a top target by new boss Xabi Alonso to strengthen his defence ahead of the new season, as Lacroix will make the short trip to play his football at Stamford Bridge for the The Blues.
Palace are already looking for a suitable replacement for Lacroix, with Augsburg's Chrislain Matsima reportedly top of the list with Trabzonspor's Chibuike Nwaiwu seen as an alternative.