The agency is also working on a campaign to promote Sony's association with the 2010 World Cup, which is being shot in 3D.
Ben Moore, Sony Europe's vice-president of communications, chose Anomaly over the incumbent after a final two-way pitch handled by the AAR.
"We were looking for a new advertising model that puts brilliant people, who instinctively understand digital but who have an agnostic view, at the heart of our approach. Anomaly will give us that," Moore said.
Anomaly will now be Sony Electronics' key strategic and creative partner, sharing the account between its UK and US offices.
Fallon has handled the estimated £50 million account since 2002 and has produced a number of iconic ads for Bravia TVs including "balls" and "paint".
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