The 185-pound bout is expected to headline UFC Fight Night on Oct. 23. UFC officials have not announced an official location for the event.
Costa (13-1) has not fought since he came up short in a title bid against Israel Adesanya at UFC 253 last September. The 30-year-old Brazilian was booked to five-round main events against Robert Whittaker and Jared Cannonier, but withdrew from both. He has expressed dissatisfaction with his contract several times this year.
Before losing to Adesanya, Costa was 5-0 in the UFC with four finishes.
Vettori (17-4-1) is also coming off a loss to Adesanya. Born in Italy and now fighting out of Huntington Beach, California, Vettori suffered a unanimous decision loss to Adesanya in a title fight in June. He immediately expressed interest in fighting Costa following the defeat.