It is understood to have beaten Bardsley and Willmott Dixon to take the project, which boasts a quirky Jenga-like design drawn up by architect Stephenson Studio.
Demolition of existing warehousing at the site on the corner of Adair Street and Great Ancoats Street is due to kick-off shortly.
The Leonardo Hotel will rise to 13 floors and is expected to cost over £25m to build.
Durham-based J H Partners is the M&E consultant with Bury-based Booth King Partnership providing structural design.