Morales is the news anchor for the "Today" show and Cohen is host of "Watch What Happens: Live."
The Miss Universe competition is to air live Sept. 12 on NBC. A live Spanish simulcast is set for broadcast on Telemundo.
"We are happy to welcome Andy and Natalie to the Miss Universe stage where they are sure to turn up the heat in Sao Paulo," Shugart said in a statement. "This year marks the 60th anniversary of the Miss Universe pageant and what better place to showcase beautiful women from around the world than in Brazil, a country that is as charming and beautiful as its people."