Italian and French media report the Bretons have paid two million euros ($2.34 million) for 26-year-old Rugani, who has seven appearances for the Azzurri.
"We couldn't hope for better. He has Champions League experience and with Italy," the French club's president Nicolas Holveck said in a statement.
In March, Rugani became the first Serie A player to test positive for Covid-19 before last season was halted due to the virus outbreak.
Earlier, Holveck's side announced the arrival of Inter Milan wing-back Dalbert Henrique, also on a temporary deal.
On Sunday, the unbeaten top-of-the-table outfit welcome second-from-bottom Reims in their final match ahead of a two-week break due to the international window.
