The Enquirer understands the fit-out deal is worth more than £20m.
Galliford Try was main contractor in charge of the £66m build for the 220,000 sqft office block on behalf of developers Arena Central Development Ltd.
Galliford Try will now complete the Category B fit-out of the building including provision of power and data systems and furnishings.
In addition, teaching spaces including auditoriums are being created on levels one and two of the building. The offices are expected to eventually accommodate over 2,000 staff.
Building West Midlands Managing Director Simon Burton said: “This contract award is testament to the excellent progress that the team has made so far at Arena Central.
“We look forward to working with ACDL and HSBC UK to provide the high-quality working environment that their employees require.”