The 41-year-old Spaniard - who last week said he was ready to return to coaching after a brief sabbatical since stepping down from the Barcelona hotseat at the end of last season - signed a three year contract on Wednesday.
Guardiola, who twice guided Barcelona to the Champions League title, will replace current Munich boss Jupp Heynckes, whose contract expires in June, just after his 68th birthday.
Bayern, who have not won any silverware in the past two seasons, have pulled off a major coup as Guardiola had been linked with jobs in England with both Chelsea and Manchester City being mentioned.
Bayern, who have won a record 22 German league titles as well as four Champions League trophies, made no secret of their delight at beating off high-profile rivals for his signature.
"We are very pleased that we have succeeded in securing the signature of Pep Guardiola, who was being courted by many clubs," enthused chairman Karl-Heinz Rummenigge.
"Pep Guardiola is one of the most successful coaches in the world and we are sure he will lend plenty of glamour, not just to Bayern, but also to German football. We look forward to working with him from July 2013."
Heynckes had told Bayern he will not be extending his contract past June and club president Uli Hoeneß paid tribute to the veteran, who steered Bayern to last season's Champions League final where they lost on penalties to Chelsea.
"After the decision from Jupp Heynckes, to whom we are extremely grateful for all his work, we would all be very happy if the team gives this coach the glorious farewell he deserves," Hoeneß said. "As an adequate replacement for Jupp Heynckes, only a coach of the calibre of Pep Guardiola could come into question."
Guardiola will be working as head coach alongside Bayern's director of sport Matthias Sammer, who joined in July from the German FA, and Germany legend Franz Beckenbauer was quick to praise the club's success in recruiting such luminaries.
"One has to say, hats off!" Beckenbauer, who enjoyed World Cup success both as player and coach with the then West Germany, told German Sky.
"Matthias Sammer and Guardiola - I don't know if you can get a better team," he said.
With Bayern facing Arsenal in the last 16 of the Champions League in February, the pressure is on the team to win some silverware after finishing both of the last two seasons without a single trophy.
"If he (Heynckes) brings the season to an end with one title or another, he will have managed an excellent farewell," added Beckenbauer.
Despite all his success at Barcelona, Guardiola - whom moody Swedish striker Zlatan Ibrahimovic once dubbed "a philosopher" as an insult - will have his work cut out at Bayern, where immediate success is demanded.
Former German national coach Jürgen Klinsmann lasted ten months before he was sacked in April 2009, while current Holland boss Louis van Gaal was dismissed in April 2011 despite winning the league and cup double, plus having reached the 2010 Champions League final.
Guardiola will have to get his German up to speed fast - and bring the much-heralded success he enjoyed at Barcelona to Bavaria.