Diana, the first wife of the heir-to-the-throne, Prince Charles, was killed when the limousine carrying her and her lover Dodi al-Fayed crashed in a Paris tunnel in August 1997.
William was 15 and Harry was 12 at the time.
"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," William (34) said in a statement on Saturday.
The princes have formed a committee to advise on the sculptor and to raise private funds to pay for the statue which will be located in a public garden at Kensington Palace.
Work on the statue will begin soon and it is hoped that the statue will be unveiled before the end of the year, the statement said.
The first permanent memorial to her, a 210-metre long fountain was unveiled in Hyde Park in 2004 after years of bureaucratic wrangling and squabbling over the design.
It had to be closed down a number of times after its opening and a committee of lawmakers later said it was "ill-conceived and ill-executed".
William announced earlier this month that he would move into Kensington Palace with his wife Catherine and children, George and Charlotte, from his current home in eastern England when he gives up his job as an air ambulance pilot to focus on royal duties full-time later this year.
