After 12 years in north London, the England international swapped Emirates Stadium for Goodison Park during the January transfer window.
A £20 million deal took him to Merseyside, with there a sense that the 28-year-old never truly fulfilled his potential with the Gunners despite making close to 400 appearances.
Walcott believes a change of scenery will help him to reach his peak, with Allardyce considered to be an important figure in that quest.
He told Everton’s official website on his thinking behind making a move: “I had that short stint with Sam with England and to see it now every day, the way the intensity of training is and how demanding it is has been great.
“I like to go into training every day and try to be better than the day before.
“Sam was one of the main reasons why I came to the club. I wanted a manager like that who could get the best out of me.
“He is eager to turn results around. There have been a few recent results like getting the draw against West Brom and then beating Leicester City where we have seen improved performances but I have come here to push Everton on. I want to improve the team and anything I can do to help, I will do so.
“Results will change, I am sure of it. We need to make sure we are ready and focused for the weekend because we need to start getting some more points in order to be more comfortable.”
Walcott has managed two goals in three outings for Everton so far and is already starting to feel settled in new surroundings – despite the Toffees’ last fixture seeing them mauled 5-1 by his former employers at Arsenal.
“I have settled really quickly,” added a man with 47 international caps to his name.
“When you get to go to events like that and you can get nice and personal with the fans, it’s brilliant.
“My experiences of Goodison, however brief so far, have been amazing and given the fact how tight it is, the fans are always behind the team. I loved it straight away.
“Having the opportunity to meet with the fans was really good. I feel like Everton can go up and up. It is the right place for me to be.”