Prince William told the 63,000-strong crowd at London's Wembley Stadium his mother would have enjoyed the tribute.
Sunday's gig marked the life of Diana, who died in a 1997 Paris car crash, on what would have been her 46th birthday.
Sir Elton John brought the concert to a close after sets by stars including Sir Tom Jones, Take That and Rod Stewart.
Prince William and Prince Harry opened the six-hour show and returned to the stage at the end of Sir Elton's final set, praising the artists for an "incredible evening".
"Thank you to all of you who have come here tonight to celebrate our mother's life on what would have been her 46th birthday," Prince William said.
"For us this has been the most perfect way to remember her and this is how she would want to be remembered."
The event was broadcast to 140 countries, with proceeds from ticket sales going to charitable causes favoured by the princess.
Prince William, 25, added that he hoped the concert had raised "enough money to make a difference".
Video tributes
The princes later mingled with the stars of the concert at the after-show party at Wembley Arena, next to the new stadium.
In a video tribute, ex-South African President Nelson Mandela had earlier praised Princess Diana's "energy, courage and selfless commitment" as he urged the crowd to "support the work that continues in her name".
Former Prime Minister Tony Blair and ex-US President Bill Clinton were also among those who paid tribute to Diana in video clips during the show, along with members of a host of charitable organisations.
"I think that in William and Harry, the qualities that made Diana special live on," said Mr Blair.
Earlier in the concert Prince Harry paid tribute to fellow soldiers serving in Iraq.
The 22-year-old had been due to be deployed in Basra, in Iraq, this year, but military commanders decided it was too much of a risk to send him there.
"I wish I was there with you. I'm sorry I can't be. But to you and everybody else on operations at the moment, we would both like to say 'stay safe'," he said.
Theatre performances
Sir Elton, 60, who famously performed a reworked version of Candle In The Wind at Diana's funeral, opened the concert with a rendition of Your Song, performed in front of a giant photograph of Diana by Mario Testino.
He was followed by 80s stars Duran Duran, who played a trio of songs including Wild Boys - which they dedicated to the princes - and Rio, one of their mother's favourites.
The English National Ballet - of which Princess Diana was a patron - brought a change of pace to the day and reminded everyone of the princess's love of the ballet with a performance from Swan Lake.
The theatrical theme continued later with a medley of hits from composer Sir Andrew Lloyd Webber.
Status Quo, Sir Tom Jones, Will Young and Joss Stone all took to the stage in the afternoon.
And Take That performed their number one hit Patience, although rumours that Robbie Williams might join them on stage proved unfounded.
Some of Princes William and Harry's favourites followed, including a poignant moment when P Diddy dedicated his hit track I'll Be Missing You to the princess.
"Ten years ago, Princess Diana went to a better place," he said. "Today we celebrate her life and I dedicate this song to her."
The evening wrapped up with entertainment from comedian Ricky Gervais, who was forced to improvise when technical problems caused a minor delay to Sir Elton's closing set.
Ticket-holders attending the event had been greeted with tight security following the recent attempted bombings in London and Glasgow.