Paris St Germain, who last reached the semi-finals in 1995, will face fellow big spenders Manchester City in the other outstanding tie, with the first leg at the Parc des Princes.
Ten-times champions Real Madrid were pitted against German side VfL Wolfsburg and Bayern Munich will face Portugal's Benfica. Both Bundesliga teams will play the first legs at home.
Barca, at home in the first leg, get the chance to avenge their defeat at the same stage two years ago when Atletico won 1-0 at home after a 1-1 draw at the Nou Camp. Atletico went on to reach the final where they lost to neighbours Real.
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However, recent form clearly favours the Catalans who have won their last six games against Atletico with Lionel Messi scoring in five of them. In all, the Argentine forward has netted 25 goals in 27 matches against them.
PSG and Manchester City have met only once before, in the group stage of the old UEFA Cup in 2008-09 when they shared a goalless draw.
Real Madrid have won their last three knockout ties against Bundesliga teams, with Bayern among the victims, but Wolfsburg coach Dieter Hecking was unperturbed.
"We have the opportunity to show our ability on the biggest stage, and we want to grasp that chance with everything we've got," he said.
"I will have to think about whether we want to approach the game with an attack-minded approach or more defensively."
Bayern demolished Benfica's rivals Porto 7-4 on aggregate last season, with a 6-1 win at the Allianz arena, although they were not taking anything for granted.
"We came through a tough tie against Juventus and need to keep going," midfielder Xabi Alonso said. "We have to respect Benfica, but we have plenty of time to analyse them."
(Editing by Ed Osmond)
