The experienced defensive midfielder, who boasts a wealth of leadership, including 41 caps for Denmark and a Premier League winners' medal with the Gunners – has signed a two-year contract with the Blues until the end of June 2028.
Norgaard becomes Everton's fourth addition of the summer transfer window following the acquisitions of Merlin Röhl, Tyrique George and Hayden Hackney.
Speaking exclusively to Evertontv after committing his future to the Toffees, Norgaard said: “There were many factors to it."
"I felt I needed a change and to play a bigger football role. When I spoke to David Moyes and others at the Club involved in the transfer, I heard about the whole project and I was very intrigued. Coming here just makes that feeling even stronger," he said.
"Also, my past experience of playing against Everton: the whole atmosphere, the fans, is something I really look forward to experience as an Everton player.
"It’s a big, big honour for me, and it's something I'll do my very best, not only on game days, but in general to remember how much it means for people who support this club. It will be my mindset to represent the Club in the best possible way.
"I can't wait to experience the atmosphere as an Everton player. Goodison was amazing. I just remember the ground was shaking – literally shaking. Then we came to the new stadium last year and I was so surprised because you often see clubs lose that intimacy and atmosphere.
"But I was so overwhelmed by how good the atmosphere was as well. So I can see that the soul from Goodison has been brought to the new stadium," he added.