The fight, which multiple sources confirmed to ESPN.com, will take place at UFC on Fox 2, the promotion's second show on the network.
It's not the first time the UFC has booked this matchup. The two were scheduled to meet in August at UFC 133 in Philadelphia, but that bout fell through when Davis suffered a knee injury.
Evans (16-1-1) will look to solidify his place as the No. 1 contender at 205 pounds. He's currently riding a three-fight win streak, including a second-round TKO win over late-replacement Tito Ortiz in August.
The former champion had been next in line to fight titleholder Jon Jones following that win, but had to postpone the opportunity due to a hand injury. Jones is scheduled to defend the belt against Lyoto Machida on Dec. 10.
For Davis (9-0), Evans represents easily the biggest test of his young career. The former collegiate wrestler is 4-0 in the UFC and coming off a unanimous decision win over Antonio Rogerio Nogueira in March.
The Evans-Davis fight is expected to headline the UFC on Fox 2 card, which takes place at the United Center in Chicago.
Brett Okamoto covers mixed martial arts for ESPN.com.