The scheme is part of Sigma's partnership with Liverpool City Council, Regeneration Liverpool, set up in 2007.
The scheme will comprise 2,600 m2 (28,000 sq ft) of retail and leisure units, including a 101-bedroom Premier Inn hotel and a 412-bedroom student accommodation building.
Sigma's commercial development partner, Neptune Developments, will now start construction before the end of the year.
Sigma chief executive Graham Barnet said: “The scheme forms part of the regeneration of the Lime Street and Knowledge Quarter areas, a project which is seen as a flagship development for the city. Together with our partner, Neptune Developments, we are delighted to help realise another objective in Liverpool City Council's broader regeneration aims."
Neptune Developments managing director Steve Parry added: "The scheme forms the first phase of our Knowledge Quarter project and will have a major impact on the gateway to Liverpool City Centre. We are aiming to bring exciting new retail and leisure operators to the area and we are already making good progress in negotiations with a number of parties.”