The German side, 2-0 ahead from the first leg, survived a predictably furious Juventus start and by the end were strolling to a 4-0 aggregate win against the team which has dominated Serie A for the last 18 months.
Second-half goals from Mario Mandzukic and Claudio Pizarro silenced the Juventus Stadium and kept the Bavarians, who were crowned Bundesliga champions with six games to spare on Saturday, on course for the treble.
Juventus had not lost a home European team since they were beaten 4-1 by the same opponents in 2009/10, and it was a reminder for that despite their domestic dominance, they still have some way before they can challenge for Europe's top honour.
"The best side has gone through, they showed that last week and here at this stadium," said Conte.
"We have only been working for 18 months," added Conte, who won Serie A in his first season in charge. "It's a moment where we have to work with what we've got."
"We were not so good defensively in the first 20 minutes and went through a few difficulties," said Bayern coach Jupp Heynckes.
"After that, we controlled the game and in the second half we launched lots of good attacks, we showed our qualities, we imposed our style of play."
Manuel Neuer came to Bayern's rescue when he fisted away a rising Andrea Pirlo free-kick from the edge of the area and Juve also threatened when Paul Pogba fired a low ball across the face of the goal but nobody was on hand to turn it in.
David Alaba, who scored in the first leg with a long-range shot which was misjudged by Gianluigi Buffon, had Bayern's best attempt with another effort from distance but this time the Juventus goalkeeper was equal to it and punched it away.
Bayern broke through in the 65th minute when Bastian Schweinsteiger floated over a free-kick and, although Buffon saved Javi Martinez's shot, Mandzukic headed in the rebound.
