Puel was dismissed by Southampton at the end of last season having faced criticism for his defensive tactics.
However, the Frenchman guided the Saints to a League Cup final – where they lost 3-2 toManchester United – and to an eighth-placed finish in the Premier League.
Michael Appleton, who took up the caretaker position after Shakespeare was sacked, will retain his role as assistant manager.
“It’s a great privilege to become the new manager of Leicester City – a club whose values and ambitions are closely aligned to my own,” Puel told the club’s website.
“The opportunity to help the Club build on its remarkable recent achievements is a truly exciting one and I’m looking forward to working with the owners, players, staff and supporters to deliver further lasting success.”
With Leicester sitting 14th, a point above the relegation zone, vice chairman Aiyawatt Srivaddhanaprabha has described Puel as the “perfect fit” for the Foxes job.
“When we began the process of identifying a new manager, the Board quickly established the profile of candidate we needed to take the Club forward and Claude Puel was a perfect fit,” he said.
“Upon meeting Claude, his attention to detail, knowledge of our squad, understanding of our potential and his vision to help us realise it were extremely impressive.
“He quickly emerged as the outstanding candidate and I am delighted we will have the opportunity to reinforce our long-term vision, aided significantly by his expertise.”