The 35-year-old veteran has won Champions League and six league titles in Manchester City, but lost his regular place last season and was loaned out to Milan in the spring.
Now City are selling him to Burnley, according to British information for five million pounds, equivalent to 65 million kronor.
Walker has signed a two-year contract with Burnley, who are trained by Scott Parker. The two were previously teammates in Tottenham and the English national team.
"When I talked to Scott and heard about his plans for the coming season, it was an opportunity I wanted to jump on", says Walker, who has 96 international matches for England, to Burnley's website.