A royal spokesman did not confirm the seven-figure cost -- reportedly at USD 6.8 million for repairs and refurbishments, but said the royal couple had paid for their own furnishings.
The bill includes extensive work on the 17th-century London palace apartment, including installing a new roof, overhauling the electrics and carrying out plumbing repairs, while work was needed to remove asbestos.
William and Kate, the Duke and Duchess of Cambridge, have taken up Apartment 1A, formerly the home of princess Margaret, Queen Elizabeth II's sister, who died in 2002.
The apartment was designed by Christopher Wren, the architect who built London's St. Paul's Cathedral.
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"This is the Duke and Duchess's one and only official residence. It is here that they plan to stay for many, many years to come," the royal spokesman said.
"We also had to take into account the fact that Kensington Palace is a scheduled ancient monument, and all elements of the refurbishment had to be agreed with English Heritage," the conservation body responsible for protecting historic sites.
"Often this meant ensuring a high standard of work in line with the historical significance of the Christopher Wren building."
William is second in line to the throne after his father Prince Charles.
Steeped in royal history, Kensington Palace, part of which is open to the public, is William's childhood home. It was the main residence for him and his brother Prince Harry until 1998.
Mourners left a sea of flowers and tributes at the palace gates after the death of Diana, their mother, in a Paris car crash in 1997.
Fter two tours in Afghanistan, army captain Harry now has a desk job coordinating army commemorative events in London.