The former Nottingham Forest gaffer replaces Martin Allen at the Walkers Stadium after he was sacked last month.
Megson has brought in former Foxes defender Gerry Taggart and Frank Burrows to work alongside him in Leicester's new-look management team.
The 48-year-old, who has been out of work since February 2006, was delighted to land the Leicester job and he has set his sights on helping the club win promotion to the Premier League.
"I am delighted to be back in management and doubly delighted that it is with a football club of the stature of Leicester City," Megson told the club's official website.
"Leicester is a Premiership club in everything but its divisional status. The stadium and training ground are both of the highest standard, whilst the support is both Premiership standard in its quality and quantity.
"In coming to Leicester I am not just working at a Championship club that is happy to plod along. This club has got ambition to get back into the Premiership and that is something that appeals to me greatly."