In a joint tribute, the royal brothers 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.
"Thank you to Ian Rank-Broadley, Pip Morrison and their teams for their outstanding work, to the friends and donors who helped make this happen, and to all those around the world who keep our mother’s memory alive."
Prince William, 39, was pictured driving in London ahead of the event, which took place at the Sunken Gardens at Kensington Palace.
It marked the first time William and Prince Harry have been pictured together since the Duke of Edinburgh's funeral in April. The Duke of Sussex flew to the UK from Los Angeles last Friday in order to complete a period of isolation before attending the event.
The date marks what would have been Diana's 60th birthday, with tributes being paid around the world to the late Princess.
Royal fans flocked to the gates of Kensington Palace to leave flowers, banners and cards.
WATCH: William and Harry reunite for Princess Diana's statue unveiling at Kensington Palace
William and Harry, who looked smart in dark suits with ties, arrived a few minutes early for the unveiling and stopped in a shrub-lined path outside the garden to chat to the chairman of the statue committee Jamie Lowther-Pinkerton.
The royal brothers set the tone for the event as they shared a laugh with their former right hand man and could be heard chatting animatedly with the ex-Army officer.
The trio spent a few minutes together before Lowther-Pinkerton ushered them down a small flight of steps and into the garden to meet their first guests.
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Harry let out a laugh of appreciation when he saw his mother's siblings and older brother William, who was a step ahead, greeted Lady Sarah McCorquodale kissing her on both cheeks and went on to warmly welcome his aunt Lady Jane Fellowes and uncle Earl Spencer.
Ever the joker Harry kissed his aunt Sarah on both cheeks then gave her two mock-pecks as she pointed her finger at him, and he also said his hellos to the rest of the Spencer family.
Beneath the statue is a plinth engraved with the Princess' name and the date of the unveiling, while a paving stone in front is engraved with an extract after the poem The Measure of A Man, which was in the programme for the 2007 memorial service for the Princess.
It reads: "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 stunning artwork, cast in bronze, shows the statue surrounded by three children and depicts Diana in the later years of her life.
In a statement, 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' 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."
When the two Dukes got into place either side of the statue William said "ready?" before they pulled off the cloth and the guests applauded.
Harry enjoyed a chat with his uncle, Charles, during the intimate ceremony.
Members of the Statue Committee there included Chairman Jamie Lowther-Pinkerton – former private secretary to both William and Harry, Gerry Farrell, Guy Monson, John Barnes from Historic Royal Palaces and Diana's close friend Julia Samuel, Prince George's godmother, who was pictured being greeted warmly by Harry.
Despite the shortened guest list, one source who attended said they felt it benefited to the occasion.
"You had two of her sisters and her brother and her sons reminiscing," they said. "It was beautiful, and more poignant arguably because it was an intimate family occasion. Had it been 100 people it might not have been the same."
The brothers were seen speaking to the Sunken Garden's designer, Pip Morrison.
Pip said of the garden: "We have worked carefully to ensure that the new layout and planting scheme complements the statue, providing a calming place for people who visit Kensington Palace to remember the Princess."
The sculptor, Ian Rank-Broadley, pictured here with William and Harry 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."
Princess Diana's brother, Charles Spencer, was spotted arriving at Kensington Palace for the statue unveiling earlier in the day.
The 9th Earl Spencer was joined by his sisters, Lady Sarah McCorquodale, and Lady Jane Fellowes, as they walked through the crowds towards the princess's former home.
Graham Dillamore knew Princess Diana and is the Gardens and Estates Operations Manager at Historic Royal Palaces.
He called the brief ceremony "intimate, moving and peaceful", and added: "To have had a lovely summer's day today with the roses and geranium in full bloom was just perfect. We were standing here in February up to our knees in mud, at that point we didn't think we would ever get to this day."
The gardener had only one wish for the statue, hoping that the late Diana would have "liked it".
He also recounted times that she would be jogging and stop for a small chat when she passed him by.
"She was often very concerned about how we were, whether we were too hot or too cold and was everyone well, and very interested in our lives and what we were doing, very sincere as well – so some very happy memories there," he said.
He then joked that she would often be "singing some ABBA song I couldn't stand", but he was "honoured" that she would spend the time with him.
Royal fans pinned flags, balloons and photos of Diana to the gates at Kensington Palace - the Princess' former home - to mark what would have been her 60th birthday on Thursday.
The Sunken Garden at Kensington Palace has been given a stunning makeover ahead of the statue unveiling.
The new layout was masterminded by Pip Morrison and it was beautifully executed by the Gardens and Estates team at Historic Royal Palaces, namely led by Deputy Head of Gardens and Estates, Graham Dillamore.
Kensington Palace also shared an illustration of the new design.
A royal fan was spotted with a special edition of HELLO! magazine.
A huge floral display, which says 'Princess Diana 60,' has been erected outside the gates of Kensington Palace.
A rare photo of Princess Diana from her childhood has been unearthed on social media. Her brother, Charles Spencer, released the heartwarming picture - taken by their late father John Spencer - on the official Twitter and Instagram pages for Althorp House.
The caption read: "Today is the 60th Birthday of Diana, Princess of Wales. Diana was born in Park House, on the Queen's Sandringham Estate in Norfolk which is seen in the background of this family photograph taken by Diana's father, the 8th Earl Spencer."