AMV's task will be to create a number of idents to be broadcast on the channel as well as redesigning the website to match the new identity.
The most recent series of idents, which feature an animated number two, were designed and created five years ago by Lambie-Nairn.
James Pestell, the head of marketing at BBC Two, said: "We've got a great tradition of mould-breaking brand identity work at BBC2. AMV has produced an idea with the flexibility and originality to be right up there with our best work."
Farah Ramzan Golant, the chief executive of AMV, said: "Brand design is one of the many strands we're developing at AMV. We're thrilled by the opportunity this presents us."
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