Kevan said: "It was a very difficult decision to leave Burnley, a huge one in fact.
"I have left Championship football behind to drop down two divisions to a club that has been having problems, but Notts County was my first club and it is a very close friend of mine that is now manager.
"I was an apprentice at the club and made my debut for them in 1986, so it is a club that is my first love in many respects.
"There is no doubt that Burnley is also a very special club and it will be a big miss for me, but I wish everyone there all the very best."