Smith has been given a contract until the end of the season.
Leicester City sacked previous manager Brendan Rodgers last week after they dropped into the Premier League's relegation zone.
A 1-0 defeat at home to Bournemouth on Saturday left the Foxes stuck in the drop zone, two points from safety.
Their next game is against champions Manchester City at the Etihad Stadium on Saturday.
Smith had been without a club since being sacked by Norwich City back in December.
Craig Shakespeare, who was an assistant manager when Leicester City won the Premier League title under Claudio Ranieri in 2016, and former Chelsea captain John Terry, are part of Smith's coaching staff.
Smith said: "I'm really happy to have the opportunity to lead the team during these final weeks of the season. The challenge in front of us is clear, but it's one myself and my coaching team have experienced before and, with the quality in this squad and the number of games remaining, it's very much achievable.
"Our first job is to rebuild confidence and instil belief in the team and I'm looking forward to getting to work with the players this week. Saturday will be a big test, but it's the kind of occasion that reminds us all what it means to be a Premier League club, competing on the biggest stages against the best players in the world. I know we'll be well supported by our travelling fans.
"We have to connect with that and give them a performance they can be proud of. We go there positive, looking for points."
Leicester chairman Aiyawatt Srivaddhanaprabha said: "On behalf of everyone at Leicester City, I'd like to offer Dean a warm welcome to the football club. His leadership, coaching and motivational qualities will be vital assets for us in the coming eight games as we fight to secure our Premier League status.
"We've endured a challenging season, but I have no doubt that we have the quality in our squad to win this fight. Dean's experience will be key to unlocking that potential, helping the team rediscover its confidence and channelling the support of our fans, who will be so important during these final eight games.
"Their support has been the foundation of everything we've achieved in these last 13 years and it will play a vital role once more in this crucial moment in our history. This is a fight we can win, together.
"I ask you to support the team, to fight with them for every goal, to inspire them to create a legacy again for this club. Every fan, every player, all our staff, we need to be behind the team and our new management team. Together we can find success this season."
