The 47-year-old has signed on a one-year rolling contract.
Thorn, a former Wimbledon, Newcastle and Crystal Palace defender takes the reins ahead of Saturday's home clash against Salisbury.
He commented: "I have been most impressed by all aspects of the Club, and the board share my vision when it comes to what our short and longer-term goals are and how we can achieve them.
“I’m extremely confident in my own strengths, particularly when it comes to man management and player recruitment, and allied with what I believe is an excellent coaching staff here at Kidderminster I am very excited at the challenges that lie ahead and look forward to starting straight away this weekend against Salisbury.”
Fans were stunned yesterday when it was revealed the club had sacked Burr.
During his time, he had delivered two sixth place finishes and were only just pipped to the title and automatic promotion to the Football League by Mansfield Town last season.
His final game in charge was Saturday's 0-0 against League One Peterborough in the FA Cup third round.
But chairman Mark Serrell said: “I’ve known about Andy and his qualities for quite some time and once we were presented with the challenge of finding a new manager, he was at the forefront of my mind.
“His contacts within the game are exceptional the entire Board have been simply blown away by his enthusiasm and desire to succeed both personally and for us here at Kidderminster."
“He knows what we want to achieve and shares that ambition totally."