After a one-sided 6-1 first leg win, the Bundesliga giants recorded a 4-1 second leg victory to ease into the last eight.
Harry Kane, who was on the bench for the first game, opened the scoring at the Allianz Arena after 25 minutes and was on target against with 54 minutes played.
Lennart Karl netted two minutes later and Luis Diaz completed the rout with his goal on 70 minutes.
Lazar Samardzic found an 85th minute consolation goal for the Serie A side.
Bayern will next face Real Madrid, in the semi-finals, after the Spanish side beat Manchester City 5-1 on aggregate.
Speaking after the game, a delighted Bayern boss Vincent Kompany said he was satisfied with his team’s performance.
"I'm proud of the lads: the performance, the goals, the energy on the pitch. That's not something to be taken for granted with such a lead from the first leg. All in all, it was a positive day for the club," he said.
On facing Real Madrid, Kompany added: "Everything is great at both clubs. It doesn't matter who is the better team at the moment. The history of both clubs, the talent on the pitch – that's something special.
"I hope we will have a positive game for the fans. Real Madrid are the best team in the history of the Champions League, so it will be a nice task for us. We want to win."
Atalanta boss Raffaele Palladino said he was proud of his team, despite the difficult defeat.
“I want to congratulate Bayern, Vincent Kompany, and wish them the best of luck," he explained.
"We faced the best team in the world and our goal was to give it our all.
"We have to accept the result with humility and compliment the opponent. We learned a lot from these two games."
Coach Raffaele Palladino admitted his side had been outclassed by "the best team in the world" after Atalanta's heavy UEFA Champions League exit to FC Bayern Munich on Wednesday.
Tottenham Hotspur delivered a much-improved performance to defeat Atletico Madrid 3-2 in their Champions League second-leg tie, even though it was not enough to reach the quarterfinals.
Enzo Fernandez admitted he is uncertain about his future at Chelsea after the club's heavy Champions League exit to Paris Saint-Germain, as frustration mounted at Stamford Bridge on Tuesday night.
Bayern Munich boss Vincent Kompany has urged his side afford to avoid being casual in the Champions League second leg Round of 16 clash against Atalanta despite 6-1 lead.
