The draw ensured bitter local rivalries would not be renewed for the time being, although it opened up the possibilities of an all German final or a Real-Barca clash at Wembley.
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A Bayern-Real meeting would also have been potentially explosive as there is a long history of stormy encounters between them.
The German pair, whose duel for domestic supremacy has sparked some acrimonious comments off the pitch, were glad to have avoided each other.
"We are happy with this draw, not because we think it's an easy one, but because the Champions League is an international competition and we wanted an international game rather than a national tie against Bayern," said Dortmund CEO Hans-Joachim Watzke.
Bayern winger Arjen Robben said before the draw: "We'd like to be kept apart from Dortmund, but you don't have a choice in these things."
The German sides will be at home in the first legs in two weeks' time with the return games one week later.
Bayern and Barcelona have surprisingly met just six times in European competition with only one win for the Catalans.
Barcelona's 4-0 thrashing at the Nou Camp in the Champions League quarter-final in 2008/09 is still fresh in the mind of Bayern chief executive Karl-Heinz Rummenigge.
"Barcelona are the benchmark for me in Europe," he said. "They have won the Champions League more than any other team in the recent years.
"They are the best team in Europe at the moment, with fantastic attacking potential. We played them in 2009 and received a real thumping.
"I remember that game well and I don't really like to think about it, because it was quite painful to watch. However, it's a wonderful opportunity to show that we have improved a lot since then. "
However, Bayern are Europe's in-form team, having already won the Bundesliga with six matches to spare and they demolished Serie A champions Juventus 4-0 on aggregate in the quarter-finals.
Dortmund had the upper hand in their group stage meetings with Real Madrid, drawing 2-2 at the Bernabeu and winning 2-1 at home.
"We have already played them twice this season and we were unable to beat them," said former Real Madrid Emilio Butragueno, now a club director.
"But we hope this time it will be different and we can get through to the final."
