Disasi, 22, was wanted by a number of French and European sides but joins the principality club on a five-year deal.
Monaco have paid a base fee of €13m with a further €2m to follow in potential bonuses.
The former France under-20 international was part of Ligue 1’s best defence in the 2019-20 season.
Not even champions PSG could boast a better defensive record than Reims, who conceded just 21 goals all season.
But his future lies in Monaco who are building an exciting project with new head coach Niko Kovac as head coach and sporting director Paul Mitchell.