The Bundesliga champions, chasing a fifth continental crown, will play Borussia Dortmund in the May 25 final at London's Wembley Stadium after an imperious performance that inflicted the heaviest two-legged European defeat in Barca's history.
Their bid for a third Champions League crown in five seasons ended in humiliation and the era during which they blazed a trail under Pep Guardiola, who will take over from Jupp Heynckes as Bayern coach next season, was reduced to a distant memory.
Last year's runners-up Bayern had effectively killed off the tie with last week's 4-0 victory in Munich and there was no way back for a toothless Barca when Arjen Robben cut inside and blasted the ball past Victor Valdes in the 49th minute.
A miserable night for the pre-tournament favourites and their fans thronging the giant arena was completed when Gerard Pique skewed the ball into his own net in the 72nd minute and Thomas Mueller, who scored twice in the first leg, nodded a third for a rampant Bayern four minutes later.
The Spaniards, last defeated in both legs of a European knockout tie in 1987, were deprived of the talents of Lionel Messi, who has yet to recover fully from a hamstring injury and was left on the bench.
Without the talismanic World Player of the Year they barely threatened as forwards Cesc Fabregas, David Villa and Pedro, and later substitute Alexis Sanchez, were helpless against a resolute Bayern defence.
"We played an outstanding game but there is a difference of Barca with and without Messi," Bayern coach Heynckes told ZDF television as the German domination of Spain was completed following Dortmund's win over Real Madrid on Tuesday.
"But it is a result one could not forecast," added the former Real Madrid and Athletic Bilbao boss.
"I know the philosophy of Barcelona and my team understood extremely well how to deploy our tactics.
"It was harder than it looked. My team was very focused... we knew what we were up against."
The statistics made grim reading for Barca.
Their biggest aggregate reverse in Europe before Wednesday was by four goals and it was their heaviest Champions League defeat at the Nou Camp since Dynamo Kiev beat them 4-0 in 1997.
They were also unbeaten in their previous 21 Champions League home matches since a 2-1 loss against Rubin Kazan in October 2009.
"We would have liked to play at the same level as Bayern but we can only congratulate them now and get back to work," Barca coach Tito Vilanova, who took over from his close friend Guardiola at the end of last season, told a news conference.
Fabregas was initially deployed in Messi's roving forward role in a three-pronged attack with Spain team mates Pedro and Villa.
Bundesliga champions Bayern were first to threaten when Robben burst clear on the left in the 13th minute but the Dutch winger was denied by a fine covering tackle from Pique.
The Spain centre back made another excellent intervention to nip the ball away from Philipp Lahm six minutes later before Manuel Neuer had to be alert to tip a long-range Pedro effort over the crossbar and Xavi volleyed high and wide when well placed.
As the half wore on and Bayern looked increasingly comfortable against Barca's aimless attacks, their boisterous fans high up in the stadium began to make themselves heard on a balmy night in the Catalan capital.
The home crowd were silenced four minutes into the second half when David Alaba sprayed the ball across to Robben on the right wing and he cut inside Adriano in trademark fashion before crashing a left-foot drive past Valdes.
Barca now needed six goals to get through and any fans looking towards the bench to see if Messi was warming up were disappointed.
The Germans even began to stroke the ball around in the style Barca have made their own in recent years, each pass being greeted with a jubilant "Ole!" from their travelling support.
Barca huffed and puffed for a goal to salvage some pride but Pique's own goal and Mueller's back-post header completed a truly awful and unprecedented night for a team often lauded as the greatest ever.
Bayern will be appearing in the final for the third time in four seasons after defeats by Inter Milan in 2010 and Chelsea last season and are on course for a treble of Champions League, Bundesliga and German Cup.
Their success at the Nou Camp may help them banish the painful memory of losing a dramatic Champions League final there against Manchester United in 1999, when the English Premier struck twice late on for a 2-1 comeback triumph.
Barca should wrap up the La Liga title in the next couple of weeks but a domestic championship is scant reward for a team which had set a new standard for European club football in recent years.
"When a team is so superior you have to congratulate them," Pique told Spanish television.
"Now we have to prepare for La Liga, finish it as soon as possible and start thinking about next season."
Dortmund reached the final after overcoming Real 4-3 on aggregate and host Bayern in a Bundesliga match on Saturday.