The 28-year-old ended his 12 season stint with Arsenal last month, and has made a strong start in his new career with the Toffees.
And he has now revealed that playing under his former England manager was one of the "main reasons" why he decided to join the Merseyside club.
Walcott said: "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.
"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.
"I want to improve the team and anything I can do to help, I will do so."