Site staff were told the news at a mass meeting on Monday afternoon.
A two-month handover will now take place as Mace takes charge under a construction management arrangement.
A Skanska statement said: “Battersea Power Station Development Company (BPSDC) and Skanska UK have mutually agreed to end their association on Phase 2 of the development, the Power Station, this autumn.
“To date, Skanska UK has managed the extensive first stage of works which includes: site preparation, enabling works, aspects of the chimney deconstruction and reconstruction, piling, substructure works and retaining structures, together with other critical infrastructure and enabling works to the main boiler house and the associated ground works for the main energy centre.
“Following the initial phase, it is now considered that an alternative construction management procurement route would better suit the next and continuing phase of the works.
“As a result, Battersea Power Station (BPS) and Skanska UK have mutually decided that the remainder of the works will not be carried out by Skanska UK and the existing contract will end in the autumn.
“In the meantime, there will be a transition period where Skanska UK will work with BPS and the supply chain to ensure that the progress of the project is not affected.”
Gregor Craig, President and CEO, Skanska UK, added: “Skanska UK and BPS have jointly agreed to part ways at this stage in the Power Station works and our efforts are now focused on enabling BPS to complete the transition as effectively as possible.
“I would like to thank the BPS shareholders for their support during the last two-and-a-half years.”
Skanska has been working since 2015 on phase two of the job without a formal contract as costs continue to escalate on work to transform the main power station building.
Mace originally bid for phase two and was initial favourite after securing the construction manager role to deliver £100m of enabling works.
Simon Jenner, Chief Operating Officer of Battersea Power Station Development Company, said: “Mace joins the project with an outstanding track record of successful delivery of major construction projects in London, throughout the UK and internationally.
“Mace has presented a first-class team and I look forward to working with them as we continue to deliver this incredible project.
“On behalf of the Battersea team, I would like to thank Skanska UK for their involvement to date.”
Gareth Lewis, Chief Operating Officer for Construction at Mace, said: “After working closely with the Battersea Power Station team during 2013 and 2014 on the engineering and the reconstruction of the Power Station’s distinctive chimneys, we are delighted to be awarded such a landmark project.
“The transformation of Sir Giles Gilbert Scott’s iconic listed building will be one of the most high profile and complex projects in Mace’s history; a once-in-a-lifetime opportunity to be part of the regeneration of such a key part of London’s heritage.
“We are looking forward to working closely with the BPS integrated team to deliver a world-class regeneration scheme.”