Christina Aguilera, Cee Lo Green, Adam Levine and Blake Shelton feature as mentors on the American version - based on the original production The Voice of Holland. It sees hopefuls perform in "blind auditions" where the judges face away from them.
The acquirement was confirmed after BBC One controller Danny Cohen reached an agreement with creator John de Mol yesterday.
"I'm absolutely delighted that The Voice will be coming to the BBC," he said. "It's a big, exciting and warm-hearted series and will be a fantastic Saturday night event on BBC One."
De Mol, owner of Talpa Media, added: "The Voice stands for a new generation in its genre and I'm delighted that in the UK it has been picked up by the BBC who really share my passion and belief in the show."
Shelton, Aguilera, Green and Levine on the NBC version, along with presenter Carson Daly.
Nick Southgate of Shed Media commented: "We're thrilled to be working with John de Mol and his team at Talpa in bringing The Voice to the UK public. It's an extraordinary show that has captured the hearts of viewers round the world and we're proud to be part of bringing it to BBC One."
Split into three phases, the competition begins with the blind auditions and battle phase, which then lead onto the final live stage of the competition.
The show's popularity in the US had sparked a bidding war for rights between the BBC and ITV.
The Voice will debut on BBC One next year.
> ITV 'rejected The Voice to keep Simon Cowell happy'