Sources confirmed the booking to ESPN.com on Tuesday. UFC 160 is expected to take place at the MGM Grand Garden Arena in Las Vegas.
Teixeira (20-2) will take an 18-fight win streak into the May contest. The Brazilian is 3-0 since joining the UFC last year. His latest victory came via unanimous decision over Quinton Jackson at a UFC on Fox event last month.
Bader (15-3) also earned a win on that January card, submitting Vladimir Matyushenko in the first round. The 29-year-old has gone 3-1 in his previous four fights after dropping back-to-back losses to Tito Ortiz and Jon Jones.
The promotion also announced that lightweights Donald Cerrone (19-5) and K.J. Noons (11-6) will meet on the card. Both fighters are looking to rebound after dropping their last fights.