It will be placed in the garden of the London palace on 1 July 2021.
The statue was commissioned by the princes in 2017 to mark the 20th anniversary of their mother's death and to "recognise her positive impact".
On Monday it will be 23 years since she was killed in a car crash in Paris.
Kensington Palace said installation of the sculpture had been delayed by the coronavirus pandemic, but it would be unveiled in the Sunken Garden next year.
It has been created by artist Ian Rank-Broadley, whose portrait of the Queen appears on all UK coins.