The La Liga leaders have been drawn against this year's surprise package, and will play the first leg away from home, while the Serie A champions take on the holders
Liga giants Real Madrid were drawn against surprise outfit APOEL and will play the first leg of their quarter-final away from home.
Elsewhere, French powerhouse Olympique de Marseille will host German outfit Bayern Munich before travelling to Germany for the second leg.
Chelsea, the only remaining Premier League outfit were paired with Benfica, and will play the first leg away at the Estadio da Luz.Finally, holders Barcelona were drawn against Serie A champions AC Milan and will travel to San Siro for the opening leg. Both sides previously met in the group stages of the tournament.
The first legs of the quarter-finals will take place on March 27 and 28, with the returns being held one week later on April 3 and 4.
The draw for the semi-finals means that the two favourites for the competition, Barcelona and Real Madrid, will only meet each other if they both reach the final in Munich.
The winner of the clash between APOEL and Madrid will face the winner of the tie between Marseille and Bayern, while either Benfica or Chelsea will have to deal with Milan or Barcelona in the other semi-final.
The semi-final first legs are scheduled to take place on April 17 and 18, while the return legs will be organised the following week on April 24 and 25.
The 2012 Champions League final will be played at the Allianz Arena in Munich on May 19 at 20.45CET.