During an emotional speech, the duke explained how Archie has given him a new perspective on life.
"I'm struck by a few things today," he told the crowd.
"Most of which is the power of the invisible role model. The person who may be sitting here today that doesn't realise that someone looks up to them, that - for that person - you inspire them to be kinder, better, greater, more successful, more impactful.
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Harry, 34, continued: "Perhaps it's the new found clarity I have as a father and knowing my son will always be watching what I do, mimicking my behaviour - one day maybe even following in my footsteps.
"But it's not just my role as a father that shows me that; it's in the people I see every day that don't realise how inspirational they are to those watching."
The proud dad then went on to talk about his mother, who died in a car crash in 1997.
"My mother, Princess Diana, was a role model to so many, without realising the impact she would have on so many lives," he said.
"You don't have to be a princess or a public figure to be a role model, in fact it's equally valuable if you're not because it's more relatable. Being a role model and mentor can help heal the wounds of your own past and create a better future for someone else."
The Diana Award is a charity that supports youth leadership, in honour of the late Princess.
"To the mentees here today, I am incredibly proud of what you've achieved, and I can safely say that my mother, who would have turned 58 yesterday, would feel the same," Harry concluded.