The England international joined the Toffees earlier this week in a £20m deal to revive his flagging career, bringing an end to a 12-year stay in North London.
Despite regularly being overlooked for selection by Wenger in the first half of the campaign, with each of his starts coming in cup competitions, Walcott says that he holds no grudges against the Frenchman.
"I've always had so much respect for him," he told reporters ahead of Everton's home match against West Bromwich Albion this weekend. "With any player, if you're not playing you're going to be upset, but you need to try and dig deep and get into that position. For whatever reason it didn't happen this year. That's why I've moved on.
"I've known [Wenger] since I was 16. To bring a young player in and to have belief in him, I can't thank him enough for that. After speaking to the gaffer, particularly Wayne [Rooney] as well, I felt like the club was on the up. The manager seems to get the best out of players, especially when first coming in.
"And just the plans for the future of the club, I felt like I wanted to be a part of it. Everton has a fantastic history and I want to make that history present. I want this club to push on and try and reach the levels I feel it can.
"Particularly with the players coming in, you get the sense that it's a club that financially can attract big players. For me, that was the main attraction. I had a brief spell with the manager with England and I wanted more of that. I want to be part of his plans."
Walcott scored 108 goals in 297 appearances during his time at the Emirates Stadium, including 19 in the 2016-17 campaign.