"A few months ago, I met him in New Hampshire. He told me that we were members of the same club. We stutter.
"It was really amazing to hear that someone like me became vice president," he said.
"He told me about a book of poems by Yeats he'd read out loud to practise. He showed me how he marks his addresses to make them easier to say out loud. So I did the same thing today.
"And now I'm here talking to you today about the future, about our future.
"We want the world to feel better. We need the world to feel better.
"I'm just a regular kid, and in a short amount of time, Joe Biden made me more confident about something that's bothered me my whole life. Joe Biden cared. Imagine what he could do for all of us.
"Kids like me are counting on you to elect someone we can all look up to. Someone who cares. Someone who will make our country, and the world, feel better."
Brayden's speech has sparked a huge reaction online, with people saying the boy's courage moved them to tears and "inspired" them.
"#braydenharrington you touched my heart man. You are more than just a kid, you spoke with bravery and love in your heart. We all needed it," one man wrote on Twitter.
"I feel that! I wanted to hug Brayden Harrington through the screen. What a great convention," another said.
"I'm not crying; you're crying. This here is the very best of America. #braydenharrington," another person commented.
"What a portrait of courage, strength, and hope," another said. "Brayden is an inspiration."
"I'm crying," another said. "Thank you Brayden."