Gallagher has signed a three-year deal at the Walkers Stadium after deciding to leave Ewood Park.
The 25-year-old came through the ranks at Blackburn, but failed to hold down a regular place in the side and spent most of his time out on loan.
Watford and Swansea were both thought to be keen on signing Gallagher, but Leicester have won the race for his signature.
Gallagher is set to go straight into the squad for this weekend's game with Barnsley.
Meanwhile, one player to leave the Walkers Stadium is Ashley Chambers who has joined Wycombe on a six-month loan deal.