The 19-year-old spent three months on loan at the Memorial Stadium last season and has made the move permanent after being released by the Foxes.
Norburn failed to make his first-team debut for Nigel Pearson's side after coming through the club's youth academy.
"I'm delighted to be joining the club on a permanent basis," Norburn told Rovers' official website.
"I've come back hoping to play more games than when I was here last time.
"On my return to Leicester I played a number of reserve games and I feel that this is an opportunity for me to push for a regular first-team spot."
