Mace, which is handling the construction programme on the job, awarded the contract t0 Martifer Construcoes Metalomecanicas after assessing two other bids.
Leading cladding and curtain walling specialist Prater is also understood to have been eyeing the New Street project.
Under the contract, thought to be worth around £15m, the Portugese firm will install the polished stainless steel rain screen facade, which has been designed to make a striking impact on the Birmingham skyline.