According to the BBC, the Toffees have paid more than £20m ($27.5m) to make the 28-year-old their second signing of the January transfer window. Walcott has signed a three-and-a-half year deal with the Merseysiders.
"I'm very ambitious and I've come here because I want the club to push to the next level," Walcott told the club's official website.
"And with the players that have come in, I feel like the next level can be reached. I'm very excited to be starting a new chapter and I felt this was the right place for me to be.
"The manager is very ambitious and I feel like the club is going in the right direction.
"Everton is a club with a great history. The fans are always passionate, they're great and I always used to find it very tough playing here.
Walcott has failed to start in the Premier League for the Gunners this season with his six top flight appearances all coming from the bench. His outings have otherwise been restricted to the club's domestic cup and European campaigns, which have impacted on his aspirations of playing for England at this summer's World Cup finals.
Following confirmation of the move, Walcott is in line to make his Everton debut against West Bromwich Albion on Saturday [20 January].
During his 12 years at Arsenal, Walcott scored 108 goals in 397 appearances in all competitions, with his last appearance coming in the 2-1 defeat to AFC Bournemouth on 14 January.
"It felt like it was time for me to move on [from Arsenal]," Walcott added. "It was sad but it's exciting at the same time and I want to reignite my career and push Everton to win things as they have done before.
"I want to be part of something and I feel like this place will offer me that."