Craig Shakespeare's side overcame the odds to knock Sevilla out of the last 16, and will now face Diego Simeone's side for a place in the semi-final.
- JENSON: Why Leicester face their mirror image - and worst possible draw
- QUARTER-FINALISTS: Power rankings and profiles
Elsewhere, reigning champions Real Madrid take on German giants Bayern Munich, while Juventus are set to do battle against Barcelona in a repeat of the 2015 final.
Borussia Dortmind will play Monaco, who dumped Manchester City out of the competition on Wednesday night.
LAST-EIGHT DRAW - WHO WILL QUALIFY?
Read the full article on eurosport.co.uk: Leicester to face Atletico Madrid in Champions League quarter-final