Speaking via video chat, Harry told the young recipients he still thinks of his mother "every day".
"There isn't a day during the past two-and-a-half decades where I haven't thought about the mark she left, not only on me and my brother, but on all of our lives," he said.
"I see her legacy in all of you. I see her legacy in a Diana Award community that spans multiple generations. I see her legacy every time I meet with families, young people, and children from all corners of the world.
"And I see my mum's legacy when I look at my own children every single day."
Prince William did not take part in the ceremony and instead wrote letters to the winners, saying his mum would have been "so proud".
The Diana Awards honour people aged between nine and 25 for their social and humanitarian work.
In his speech, Harry added, "Today we're reflecting on what would have been my mother's 61st birthday.
"And this year, it's also 25 years since her passing."
He shared that Diana instilled in her sons a "drive to speak up and fight for a better world".
"Now, as a husband and a parent, my mother's voice is even stronger in my life," he added.
"I know the memory I hold of my mum will never fade, because I see her spirit in each of you. So thank you for keeping her fire alive."
In William's letter, he added, "I hugely admire your efforts. Your stories are remarkable.
"Many of you face huge challenges in the face of difficult times, yet you are tirelessly breaking down barriers to create a better future for us all.
"Thank you for your compassion, bravery and absolute determination.
"You truly are the personification of my mother's legacy and I know she would be so proud of you all."
Harry and William were last seen together at the Queen's Platinum Jubilee, however, they did not acknowledge each other or even look at one another.
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