Willoughby, whose reality TV pedigree includes presenting Dancing on Ice and The Xtra Factor, will team up with Radio 1's Yates to front the talent contest and interview the competing acts and celebrity coaching panel.
"I'm so excited to be hosting The Voice," said Willoughby.
"When it launched in America I watched one of the shows and thought it was just a fantastic format, and when I heard it was coming to the UK I thought to myself how incredible it would be to be a part of it.
"It's going to be one rollercoaster of a ride and I can't wait to get started!"
Yates added: "I'm so delighted to get this job and be part of such a credible music show. The format of The Voice in America has worked brilliantly, and I have no doubt it will be just as successful on British TV."
BBC One controller Danny Cohen described Willoughby and Yates as "the perfect partnership".
"They are both big fans of the show and will bring a huge amount of passion and enthusiasm to the production," said Cohen.
Jessie J is currently the only coach confirmed for the series. The US version on NBC features Cee Lo Green, Christina Aguilera, Adam Levine and Blake Shelton.
Stars including Mark Owen, Tom Jones, will.i.am and Lenny Kravitz have all been linked to the UK show.
The Voice UK will launch in spring 2012 on BBC One.
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