England U17 international King signed the deal after turning 17 this week.
“It's something I've been dreaming about for a long time," King said. "So it's always good to achieve something that you've always wanted to achieve. So I'm happy about that.
“It's a good day to celebrate my birthday. It’s in the top one birthdays, for sure.”
Meanwhile, teammate Ife Ibrahim has also penned a first pro contract.
He said: “I think it's a blessing, you know, a great opportunity. Not many people get to sign a professional contract, so I'm very grateful and blessed to be here.
“I came here when I was at the age of seven. I went through the pre-academy stage and then got signed at the age of nine. I've been here ever since.
“I always say it's a privilege. Arsenal's a very big club, so I'm very blessed to be here and continue my journey and make it."