Having won last week's first leg 1-0 in Madrid, Real won the semi-final 5-0 on aggregate as Pep Guardiola's Bayern suffered their heaviest home defeat in European competition on Tuesday. (Agencies)
Bayern had previously never lost at home by more than two goals in Europe as the Bavarian giants saw their dreams of reaching a fourth Champions League final in five years crushed.
"We have witnessed a debacle, we didn't put enough passion into it," said Bayern chairman Karl-Heinz Rummenigge.
"We have to keep our nerve and stay rational."
Real Madrid is now one game away from 'La Decima' - their 10th European title - and will face either neighbours Atletico Madrid or Jose Mourinho's Chelsea in the May 24 final in Lisbon.
Real centre-back Sergio Ramos produced two early bullet headers to dismiss Bayern's dreams of becoming the first team to defend the Champions League title.
World Player of the Year Cristiano Ronaldo made it 3-0 at the break before the Real superstar netted his 49th goal of the season with a free-kick just before the final whistle.
Having now netted 16 times in this season's Champions League, Ronaldo set a new record for the most goals in a single European campaign, bettering the previous mark of 14 set by Barcelona's Lionel Messi and ex-AC Milan forward Jose Altafini.
There was a minute's silence before kick-off for former Barcelona coach Tito Vilanova, who died on Friday at the age of 45, and Vujadin Boskov, the former Real coach who passed away on Sunday aged 82.
Having won last week's first leg 1-0 in Madrid, Real won the semi-final 5-0 on aggregate as Pep Guardiola's Bayern suffered their heaviest home defeat in European competition on Tuesday.