The agency fought off competition from Karmarama and 101 at pitches which took place after Easter last month.
Adam & Eve/DDB was also shortlisted but pulled out of the process, which kicked off in February and was run by AAR.
Leo Burnett is the incumbent on the account. The agency picked up the business in 2011, when it was reported to be worth £12 million.
Last year Freeview launched Freeview Play, a video-on-demand and catch-up TV service, in October.
Owen Jenkinson, the marketing director at Freeview, said: "We're thrilled to be working with Anomaly who demonstrated excellence in strategy, comms planning and creativity throughout the whole process.
"We look forward to working with them to help make Freeview Play the new normal way of watching TV."