The 18-year-old has penned a five-year deal at the Emirates after a breakthrough first campaign with the senior team.
"I'm so proud and happy," Lewis-Skelly told the Arsenal club website.
"I know those words are simple, but I think they sum up how I feel signing for this club. I'm a fan and it's like a dream come true.
"I've embodied the values of Hale End and come through. I've still got a lot of years ahead of me, so if I can keep staying humble and being a good person, that's the most important thing to me."
Lewis-Skelly broke into Arsenal's first team in December and established himself as Mikel Arteta's first-choice left-back.
He made 39 appearances across all competitions, with 23 of those coming in the Premier League.
Lewis-Skelly received his first senior England call-up in March and became the youngest player to score on their debut as he netted in a 2-0 win over Albania at Wembley.
"I know I've taken a lot of experience from the games about the positive moments, the mistakes that I've made," he added.
"I'm definitely more ready now for the next season. I just want to keep learning and keep improving.
"I want a legacy. I want to win everything there is to win in the game. I want to win trophies on the biggest stages whilst being a person that's always learning and stays grounded, which is so important."