The firm has a strong US presence – its biggest customers include Intel and Texas Instruments – and is listed on Nasdaq and the London Stock Exchange.
Brunswick won the account after a three-way pitch against the incumbent and Finsbury. The account is led by Brunswick partner and technology team head Tom Buchanan, reporting to Beckloff and ARM chief financial officer Tim Score.
FD managing director Sarah Marsland led the ARM account, which the agency held since shortly after ARM's flotation in 1998.
The company announced it would review the account after Marsland went on maternity leave in January.
Last year ARM paid £550m to acquire US rival Artisan Components.