The brothers were joined by Diana's siblings, Lady Sarah McCorquodale, Lady Jane Fellowes and Charles, the 9th Earl Spencer, at the small ceremony.
The brothers were pictured walking side by side into the Sunken Garden at Kensington Palace, with Harry grinning and looking relaxed.
Earl Spencer, Lady Sara, and Lady Jane were pictured walking through the crowds which had assembled outside the palace on Thursday afternoon.
During the small, private ceremony, the statue was unveiled, including words on a paving stone underneath it which read: "These are the units to measure the worth/Of this woman as a woman regardless of birth./Not what was her station? But had she a heart?/How did she play her God-given part?"
The verse is an extract from the poem The Measure of A Man, which featured in the 2007 memorial service for the princess. It has been adapted to read about a woman instead of a man.
In a rare joint statement, Prince William and Prince Harry said: "Today, on what would have been our mother’s 60th birthday, we remember her love, strength and character — qualities that made her a force for good around the world, changing countless lives for the better.
"Every day, we wish she were still with us, and our hope is that this statue will be seen forever as a symbol of her life and her legacy.
They went on to thank the "friends and donors who helped make this happen, and to all those around the world who keep our mother’s memory alive."
William and Harry were greeted as they arrived at the garden by Jamie Lowther-Pinkerton, who was the chairman of the small statue committee and could be heard laughing with him, setting a relaxed tone for the event.
Lowther-Pinkerton was the brothers' right hand man for many years.
The brothers greeted their family members and members of the committee who attended the event, with Harry kissing his aunt Lady Sarah on both cheeks and greeting his other aunt, Lady Jane, and his uncle, the Earl Spencer, warmly.
Harry and William each took a side of the fabric covering the statue. William said "ready" before they pulled it down as guests applauded.
In a comment after the event, sculptor Ian Rank-Broadley said: "Diana, Princess of Wales was an icon who touched the lives of people right around the world, so it has been a privilege to work alongside Prince William and Prince Harry on this statue which commemorates her life.
"We wanted to capture her warmth and humanity while showcasing the impact she had across generations. I hope that people will enjoy visiting the statue and the Sunken Garden, and taking a moment to remember the princess."
Explaining the statue, Kensington Palace said: "The statue aims to reflect the warmth, elegance and energy of Diana, Princess of Wales, in addition to her work and the impact she had on so many people.
"The figure of Diana, Princess of Wales is surrounded by three children who represent the universality and generational impact of the princess’s work. The portrait and style of dress was based on the final period of her life as she gained confidence in her role as an ambassador for humanitarian causes and aims to convey her character and compassion."
The statue is 1.25x life size, and was cast by Castle Fine Arts Foundry in the traditional “lost-wax” process with a patina of a bluish green over black. The cast is hollow and is supported by a stainless-steel armature, the palace team added.
Ahead of the event, Kensington Palace redesigned the garden, filling it with thousands of flowers including Diana's favorites, forget-me-nots. The flowerbeds were made deeper and the lawn extended to make the area calmer and more reflective.
The statue will be a permanent part of the garden, which was one of Diana's favorite spots. She lived in Kensington Palace throughout her marriage to Prince Charles and after their separation.
The statue was first commissioned in 2017 and has been delayed in part by coronavirus.
William and Harry have had a difficult relationship over the last 18 months, with tensions particularly strained since Harry and wife Meghan Markle announced they planned to step back from their senior royal duties in January 2020.
Even before that, Harry had said he and William were "on different paths," during an interview with ITV's Tom Bradby in South Africa in October 2019.
It has been suggested the feud started when Harry was dating Meghan, because William encouraged him to take his time.
Reports in recent months have suggested William was furious when he heard allegations of bullying by Meghan of palace staff. She has denied the allegations, which were made public ahead of the interview she and Harry did with Oprah Winfrey.
But ahead of the unveiling, biographer Omid Scobie said the rift was not as bad as some reports have suggested.
He told Good Morning America: "The relationship between Harry and William is still extremely complicated.
"From what I understand from sources it is just a case of distance. They're simply not talking at the moment and while there has been small communication leading up to this point through their relevant teams, this is really going to be the first time where they have a proper opportunity to chat to each other."
Rhiannon Mills, Sky's royal correspondent, said the smaller ceremony was something the brothers wanted because of the strain in their relationship.
She said: "They all know all eyes are going to be on them.
"Harry is very well-schooled when it comes to putting on appearances. Both brothers are wary of the press and will not want to stoke any stories about them falling out."
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