The two princes said that "the time is right to recognise her positive impact" with a permanent statue.
The sculpture will be erected in the public grounds of her former residence, Kensington Palace.
A sculptor has yet to be chosen but a spokesperson said work on the artwork would begin soon.
'Reflect on legacy'
Princes William and Harry said in statement: "It has been 20 years since our mother's death and the time is right to recognise her positive impact in the UK and around the world with a permanent statue.
"Our mother touched so many lives. We hope the statue will help all those who visit Kensington Palace to reflect on her life and her legacy."
The Queen has said she "supports" her grandchildren commemorating Princess Diana.
The announcement comes after Prince William said his mother's death made him "very angry".
The rare admission was made during a visit to a London bereavement centre.
The Princess of Wales died on 31 August 1997 in a car crash in Paris, when the Duke of Cambridge was 15 and his brother was 12.
Her death led to an international public outpouring of grief, marked by millions of tributes being left at royal residences for many months.
It is thought her funeral was watched by 2 billion people worldwide.
In July 2016, Prince Harry said he did not talk about his mother's death "for the first 28 years of my life".