The Battersea Power Station Development Company said the deal could be worth up to £750m.
Skanska is expected to commence the enabling packages for the main works in March 2015 with works on the Power Station scheduled for completion in 2019.
The iconic project to redevelop the old power station also attracted bids from Balfour Beatty, Lend Lease and Mace.
Mace started out as favourite after securing the construction manager role to deliver £100m of enabling works, including demolishing and rebuilding the existing chimneys and restoring the historic structure.
The site handover from Mace to Skanska will be completed by the end of next month.
Philip Gullett, Chief Operating Officer at BPSDC, said: “Skanska’s appointment to restore and refurbish the Power Station is further demonstration of our shareholders’ commitment to the development and a major step towards opening up the Battersea Power Station to the public.
“Skanska is a leading contractor, with the experience and expertise to undertake the work required on this Grade II listed iconic building.”
Developers said work overseen by Mace since October 2013 has seen:
• The chimney dismantling and rebuild programme is on schedule and led by specialist engineers Beroa Bierrum, working with Delta, the specialist dismantling contractor. The South West chimney – the first to be dismantled before being rebuilt, is down to a height of 20m from its full 50m height. It will be rebuilt and back to full height by the Summer of 2015;
• Extensive brick work surveys have been undertaken on the Power Station elevations by specialist contractors PAYE Stonework & Restoration Ltd – ahead of the brickwork repairs;
• Structural repairs to the steel and brick work on the four wash towers beneath the concrete chimneys – led by J.Coffey Construction Ltd – are also progressing to schedule;