The sale follows BAM letting the 30,600 sq ft building to technology firm NVidia, in May.
It has been bought by investment and asset management company Threadneedle UK Property Trust.
The transaction is expected to be completed on 1 August.
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Martin Hill, BAM Properties' Development Director, said: "Its great news that we've reached a deal with Threadneedle. The quality of the building and the strength of the tenant are obviously major attractions for the new owner.
"BAM not only developed the building Aztec West, we also designed it and constructed it, so we know the building inside out and are confident that it will serve its landlord and their tenants well."
Hartnell, Taylor, Cook were the agents for BAM, while Colliers International represented Threadneedle.
The transaction was valued at £5.6m.
(CD/JP)
