Barcelona will face Arsenal in the quarter-finals while Manchester United take on Bayern Munich.
Titleholders Barcelona will play Arsenal in the quarter-finals of the Champions League and remain on course for a repeat of last year's final against Manchester United after the draw was made on Friday.
United will travel to Bayern Munich for the first leg of their quarter-final in a rematch of the 1999 European Cup final, where the English Premier League side snatched two goals at the death for an extraordinary 2-1 win.
"This is a very difficult but also an attractive draw," Bayern's director Karl-Heinz Rummenigge told his club website [www.fcbayern.de].
"Manchester are a team that is up there at the very top. We will have to reach our limits and even exceed them if we want to progress. Manchester are the favourites and that is where it is attractive in that we can trip up the favourite."
The winners will face Olympique Lyon, conquerors of Real Madrid in the previous round and Liverpool in the group stage, or Girondins Bordeaux in the semi-finals after the two French clubs were pitted together in the last eight of the draw made at UEFA's headquarters in Nyon.
Inter Milan's reward for knocking out Chelsea is a quarter-final against CSKA Moscow, with either Barcelona or Arsenal waiting if they get past that hurdle.
Barcelona's match against Arsenal is a repeat of the 2006 final which the Spanish club won 2-1 in Paris. The London club will host the first leg.
The draw featured teams from six countries, the first time since 1998-99 that so many nations have been represented in the last eight.
Bordeaux president Jean-Louis Triaud told Eurosport: "We were chatting with [Lyon president] Jean-Michel Aulas before the draw and agreed we did not want to face each other.
"But it [the draw] means at least that there will be a French club in the semi-finals and they will have the advantage of playing at home in the return leg," he said.
"It will be a peculiar tie," Aulas told Eurosport. "But it will mean there will be a French side in the last four for the first time since Monaco."
Monaco were the last French side in the Champions League last four, knocking out Chelsea before losing 3-0 in the final to Jose Mourinho's Porto in 2004.
The quarter-final first-leg ties will be played on March 30 and 31. The final will be played at Real Madrid's Bernabeu stadium.
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