The organization officially announced the fight on Saturday, and it is expected to take place on the preliminary card of the event, which takes place from The Pearl at the Palms Casino in Las Vegas on June 4.
Each fighter has lost in their only appearance under the Zuffa banner. Rivera debuted in the WEC last November, where he suffered a first round knockout loss to Erik Koch. The loss was the first of his career.
Duran, meanwhile, made his UFC debut earlier this month at UFC on Versus 3. Taking on Takeya Mizugaki, Duran dropped a tough split decision loss to snap a four fight win streak.
The Ultimate Fighter 13 Finale will air live on Spike TV, headlined by a lightweight bout between Anthony Pettis and Clay Guida.