The France international has cost Chelsea £38m and becomes their sixth summer signing after Christopher Nkunku, Nicolas Jackson, Lesley Ugochukwu, Angelo Gabriel and Diego Moreira.
Chelsea went into the market for a new central defender after Wesley Fofana suffered an ACL injury that will likely keep him out for most of the 2023/2024 season.
Disasi spent three years at Monaco, having joined them from Stade Reims in August 2020.
The 25-year-old made 129 appearances in total for Monaco.
"I am really proud to be able to be a part of this great family," Disasi told Chelsea's website.
"I hope to achieve very big things here. To win titles. I will do everything I can to achieve those objectives. I am very ambitious."
"I can't wait to feel the energy of the fans."
"The fervour of the fans in the Premier League, the atmosphere, the intensity of the games - it is something that excites me."
Disasi has played four times for the France national team, including three times at the 2022 FIFA World Cup in Qatar.
Co-sporting directors Laurence Stewart and Paul Winstanley told the club's website: "Axel has showcased his quality over several seasons in France and that has deservedly led to recognition on the international stage.
"He is ready to take the next step in his career and we are delighted that will be with Chelsea. We welcome him to the club and look forward to him joining up with Mauricio Pochettino and his new teammates in the days ahead."
