Walcott completed a £20 million switch to Goodison Park on Wednesday, putting pen to paper on a three-and-a-half-year deal.
The forward scored 108 goals in 397 appearances for the Gunners, winning three FA Cups under Arsene Wenger's stewardship.
And Walcott paid tribute to the Arsenal fan base after sealing his move to Everton, thanking them for their messages of support following his departure.
In a video message posted on Twitter, he said: “I just want to say a massive thank you to all the Arsenal fans.
“I've been so overwhelmed with the messages I have received today of good lucks and I can't thank you enough, and especially for the last 12 years.
“I just want to wish everyone at the club all the best for the future.”
Walcott is Everton's second big-money signing in the January to date with Cenk Tosun having arrived from Besiktas for £21m earlier in the transfer window.
Stanmore-born Walcott, who has earned 47 England caps, could return to Arsenal as early as February when Everton travel to the Emirates Stadium next month.