The venue, which is to be built close to the Etihad Stadium, would be the largest arena in the UK and sustain 3,350 jobs during construction.
BAM beat rival bids from Sir Robert McAlpine and Laing O’Rourke.
Alongside BAM, the professional team for the £350m scheme includes architect Populous, structural consultant BuroHappold, M-E Engineers as building services consultant, acoustic consultant Vanguardia and cost consultant Turner & Townsend.
Subject to successful planning approval, which has just been submitted, it is envisaged the venue would take three years to build, with the first events planned to be held in 2023.
Tim Leiweke, chief executive of Oak View Group, said: “I’m thrilled that we have put together a project team of such calibre, and with such strong links to the beating heart of the North West – Manchester.
“While we are living in uncertain times, we know that Manchester and its people are resilient.
“Manchester has become a vast and vastly impressive city. Nevertheless, this visionary development will stand out for a long time to come.”