Bayern will now face fellow German side Borussia Dortmund in the final at Wembley on May 25 after they overcame Real Madrid over two legs.
Die Welt's editorial said the semi-final results had given Germany a "reason to be proud", with a German winner for the first time in 12 years now guaranteed.
It added: "Bayern humiliated their opponents for the second time in the space of a week, doing the things which had set Barcelona apart, only better."
German tabloid newspaper Bild wrote: "For the first time in the history of the Champions League, there will be an all-German final. It was a demonstration of power against what once was the best team in the world."
The Frankfurter Allgemeine Zeitung hailed a "dream final", continuing the general feeling that Bayern and Dortmund have "humiliated" Spanish football.
"Fussball is coming home" found its way onto the front page of the Suddeutsche Zeitung, which dedicated several pages to Bayern's monumental triumph.
Arjen Robben's goal to make it 1-0 put the victory beyond any doubt, so much so that, according to the Suddeutsche, "anybody who still believed Bayern would be eliminated would also believe that they would start driving on the right in England".
In contrast to the euphoria and acclaim of the German press, the media in Spain were understandably less impressed by the performances from a Barca side who have widely been regarded as the best team in the world over the last five years.
Catalan-based daily Sport led with the headline "Barca, humiliated and out of Europe", adding in their copy: "Barcelona said goodbye to the Champions League in the cruellest and most painful way possible: suffering another heavy defeat against Bayern who, on aggregate, have unloaded on them 7-0."
El Mundo Deportivo, whose base is also in Barcelona, preferred to praise "great" Bayern with their headline but were also far from complimentary about the performance of Tito Vilanova's side, who the paper described in their copy as "impotent" against the German outfit and lacking belief they could overturn the 4-0 first-leg deficit without Lionel Messi, who was an unused substitute having struggled with a hamstring problem in recent weeks.
The paper also said: "Tito Vilanova's team surprisingly eased off in the second half thinking already about the league," referring to the fact Barca could clinch the Primera Division title this weekend.
The two Madrid-based sports papers, Marca and AS, followed a similar line as they both hailed Bayern while describing Barca as: "impotent", "humiliated by a cyclone", "grey, without bite, inane and soulless".