The defender is set to move to Stamford Bridge in a deal reportedly worth £45 million and will be another option to cover for injured compatriot Wesley Fofana.
Disasi is expected to compete for the centre-back position with the likes of Thiago Silva, Trevoh Chalobah and Levi Colwill, while another Frenchman Benoit Badiashile is preparing to return from a hamstring injury early in the season.
Fofana is likely to miss much of the season after anterior cruciate ligament (ACL) reconstruction surgery in July.
Disasi has four caps and was first called up for the 2022 World Cup in Qatar, making his France debut in the 1-0 group stage defeat by Tunisia.
Chelsea are looking to revive their fortunes under new manager Mauricio Pochettino after coming 12th in the standings last season - their worst finish since 1994.