The announcement was made by Donald Trump, NBCUniversal and Miss Universe President Paula M. Shugart.
Cohen is the host of Bravo's "Watch What Happens Live" and Rancic is co-anchor of "E! News."
The 61st annual Miss Universe competition is to air live on NBC Dec. 19 from PH Live at Planet Hollywood Resort & Casino.
"The Miss Universe competition heads to Las Vegas for what will be another exciting show for our fans and contestants," said Shugart in a statement. "Andy and Giuliana are the perfect duo and the ideal hosts for this show. It's obvious they have a lot of fun on stage, which in turn makes it a great experience for the audience. We look forward to collaborating with them and our partners, Planet Hollywood Resort & Casino, on this worldwide telecast."