Joint developers Argent and the Greater Manchester Property Venture Fund, which is part of the Greater Manchester Pension Fund (GMPF), opted for Carillion over BAM and Kier for the 281,000 sq ft office scheme.
Kieran Quinn, chairman of GMPF, said: "We underwent a vigorous and lengthy process to ensure that the right contractor was selected for the construction of One St Peter’s Square.
"Experience, reputation and ability to deliver were of paramount importance as we are committed to ensuring that this is a very high quality scheme and that it is completed within the projected time frame.
John Rodaway, accounts director at Carillion, said: "We are delighted to have been selected as the contractor for this high profile development. One St Peter’s Square is not only a building of significant architectural merit but it will also create a new landmark building at the gateway to the city centre.
"We have previously worked with Argent and we are very happy to have the opportunity to continue our successful working relationship."
Argent project director James Heather added: "While we are delighted to have a 63,000 sq ft pre-let to KPMG, we still have almost 210,000 sq ft of Grade A office space available.
"As one of the only developers currently speculatively building commercial property outside of London it further reinforces our commitment to the scheme and confidence in its unique offering and setting."
Connell Brothers is carrying out the demolition of the existing building, due to be completed by April, when Carillion will start work.
One St Peter’s Square will be ready for handover to the occupiers by spring 2014.