The England international left the Gunners to kickstart his career on Merseyside in January, 12 years after being brought to North London by Wenger.
Following last week's announcement that the 68-year-old is to leave Arsenal next month, Walcott praised his former manager and admitted that he is now also keen to repay current boss Sam Allardyce.
"Just a word on Arsene after announcing he is leaving Arsenal, he is a fantastic man, fantastic manager," he told Sky Sports News after scoring the only goal in Everton's 1-0 win over Newcastle United on Monday night.
"I can't thank him enough for what he did for me at such a young age to have that faith in me, and now I'm here with Sam and again he's shown so much faith in me.
"I just want to repay that really to him personally and for this team. I want to work hard. I feel like the team and myself worked really hard tonight and like I say it was a really well-fought battle tonight."
Walcott netted 108 goals for Arsenal before joining the Toffees in a £20m deal at the start of the year.