The landmark deal allows this first phase office building for accountant KPMG to start at the Sovereign Street site.
There are also plans for two further new buildings and public green space created on the site of the former Queen’s Hall.
The site was originally earmarked for two skyscrapers but the £115m Criterion Place project was abandoned in 2008 following the property slump.
David Wells, development director at Muse, said: “The regeneration of Sovereign Street has been a long held ambition of the Council, and we are delighted be playing a major part in making this a reality.
“We now look forward to managing the construction of the building for KPMG, which will be open by September 2015.”
Sovereign Street has been a council-owned car park since the Queen’s Hall was demolished in 1989. In close proximity to the city’s waterfront area, railway station, city centre and retail core, it forms a key part of the Council’s plans to enhance and regenerate the southern part of the city centre.
A planning application was approved in December 2012 and construction will shortly commence. Morgan Sindall has been selected as contractor for the building. Jones Lang LaSalle acted for Muse and Allsop for British Steel Pension Fund.