The princes greeted an estimated 70,000 fans at the venue — and millions more watching the event live worldwide — to thank them for coming.
"This evening is about all that my mother loved in life: her music, her charity and her family and friends," William said. Harry added a special message for his army unit, currently serving in Iraq.
"I would also like to take this opportunity to say hi to all the guys in A Squadron of the Household Cavalry, who are serving out in Iraq at the moment.
"I wish I was there with you. I'm sorry I can't be. But to all of those on operations at the moment, we'd both like to say 'Stay safe."'
Harry, a second lieutenant in the regiment, was banned from going to Iraq for security reasons.
The crowd cheered as Elton John took to the piano to sing "Your Song" — and took to its feet as the princes introduced one of their mother's favorite bands, Duran Duran.
The princess died Aug. 31, 1997, along with her boyfriend Dodi Fayed and their driver when their Mercedes crashed inside the Pont d'Alma tunnel, while media photographers pursued them.
The memorial concert features music from some of Diana's favorite acts, including Tom Jones, but will also host younger performers including Kanye West, P. Diddy, Joss Stone and Lily Allen.
"Pray for sun!" Duran Duran lead singer Simon LeBon told the crowd as the band broke into "Sunrise," followed by "Rio," which they dedicated to Diana.
Security for the event was increased after on Saturday that involved a Jeep Cherokee slamming into the main terminal and bursting into flames.
Police said they believed Saturday's attack was linked to the car bombs, and Britain raised its terror alert to "critical" — the highest possible level. At least 450 officers were on duty to police the concert.
The show also includes a performance by the English National Ballet and songs by Andrew Lloyd Webber in honor of Diana's love of dance and theater.
A family of fans from Portsmouth in southern England said they had come to sample the wide variety of acts all playing under the same roof — but that the memory of Diana's death was also in their minds.
"I was devastated," Karen Moore, 50, a restaurateur, said of Diana's death.
Her husband, David, 52, and the couples' daughters, Lucy, 23, and Katie, 21, said they were there for the music, but also wanted to express their sympathy for the princes.
"William and Harry are the same age as us," Lucy said.
Diana is remembered for her glamour, for her extensive charity work — and for her tempestuous marriage to Prince Charles, heir to the British throne. The pair married in 1981 in a ceremony watched by millions around the world, but divorced in 1996 after admissions of adultery on both sides.
William said the concert was a chance for people to "remember all the good things about her because she's not here to defend herself when she gets criticized."
"After 10 years, there's been a rumbling of people bringing up the bad, and over time people seem to forget — or have forgotten — all the amazing things she did and what an amazing person she was," William said in a British Broadcasting Corp. interview, which was recorded earlier this month and broadcast Friday.
Tickets for the concert cost $90 with proceeds going to causes Diana supported, including land mine and AIDS charities.
Harry, 22, said the brothers had asked Elton John to play "Candle in the Wind," the song he played at Diana's funeral in Westminster Abbey. Originally about Marilyn Monroe, its lyrics were reworked in tribute to Diana, and it became a worldwide No. 1 hit in 1997.
A memorial service is also planned in London on Aug. 31, the anniversary of Diana's death.