Craig Shakespeare's side avoided the likes of Real Madrid and Barcelona but, having seen off the challenge of Sevilla in the last-16, they will return to Spain in the last-eight.
The Premier League champions, who are fighting to avoid relegation from the top-flight this season, will travel to Atletico's Vincente Calderon for the tie’s first leg on Wednesday 12 April.
The return leg will be played the following week, on Tuesday 18 April at the King Power Stadium.
“Atletico Madrid are a very good team with some fantastic individuals with experience in the competition, but we'll be ready to give everything to progress,” Shakespeare said.
“It will be a brilliant occasion for our supporters and for everyone at the club, but before the players can begin to think about these games, we have Premier League matches to come that are of huge significance to our season.”
Barcelona’s remarkable comeback against Paris Saint-Germain in the previous round has led to a repeat of the 2015 final, with Luis Enrique’s side set to play Juventus.
Champions League quarter-final draw
Atletico Madrid vs Leicester City
Borussia Dortmund vs AS Monaco
Bayern Munich vs Real Madrid
Juventus vs Barcelona