The Grade II listed building, the four towering chimneys of which have long been a key feature of south London's skyline, will become home to some 1,400 staff, the company announced.
It follows a multibillion-pound restoration of the former electricity generator, which has stood unoccupied for decades on the banks of the River Thames.
Apple will become the largest office tenant in the new-look development, taking up around 40% of the space and spreading staff across six floors.
Employees will be relocated from various London offices in 2021, Apple said.
It added that it was a "great opportunity to have its entire team working and collaborating in one location while supporting the renovation of a neighbourhood rich with history".
Rob Tincknell, chief executive of Battersea Power Station Development Company, said: "We are delighted that Apple has chosen to make Battersea Power Station its home in 2021.
"It is testament to our fantastic building and the wider regeneration of the 42-acre site which offers a carefully curated mix of homes, businesses and leisure amidst extraordinary open spaces and new transport links.
"It has always been our clear objective to create one of London's most thriving new communities and this commitment from Apple will undoubtedly help us achieve our goal."
Approximately 500,000 sq ft will be used by Apple in the central boiler house of the former coal-fired power station.
London Mayor Sadiq Khan said: "I am delighted that Apple is moving into Battersea Power Station, helping to generate new jobs and economic prosperity for Londoners.
"It is a further sign that London is open to the biggest brands in the world and the leading city for trade and investment."
Chancellor Philip Hammond said: "Apple's decision to move 1,400 staff to a new campus at Battersea Power Station further strengthens London's position as a global technology hub, and demonstrates how the UK is at the forefront of the next steps in the tech-revolution.
"It's another vote of confidence in the UK economy, sending a clear signal that companies are continuing to invest in Britain's future, and that we are one of the most attractive investment destinations for the global technology industry."
Apple's European headquarters will remain in Cork, Ireland.
As part of the redevelopment of Battersea Power Station, the historic chimneys have each been brought down temporarily and will be rebuilt using the same technique by which they were originally erected.
Currently, three of the chimneys have been brought down to the base while the fourth, the south-west chimney, has already been returned to its former height.
All the chimneys should be approaching full height by the end of the year and will be painted in 2017, developers said.
They added that one of them will also boast a viewing platform upon completion.
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