Molby lead the Harriers to the Conference title after being appointed manager in 1999, but controversially left the club to take over at Hull City in March 2002.
His time in East Yorkshire ended when he was sacked after just seven months, and he has been out of football since.
Harriers chairman Colin Youngjohns said it was a difficuly decision to sack Britton, but insisted there were no hard feelings between the club and Molby - blaming Hull City for his acrimonious departure.
He said: "We had to make changes sooner rather than later to ensure we protected our Football League status.
"I know some people will question why we have turned to Jan to take over the vacant position after he left in controversial circumstances.
"I said at the time of his departure we could fully understand with Jan wanting to test himself on a bigger stage at Hull.
"We had no problem with Jan although we were upset with the way we believed Hull approached the matter at the time.
"When we made decision to change the manager we had to look at who was best equipped to make an immediate impact. Whatever anybody says Jan did a terrific job during his first stint here."