Guardiola will move to Germany in the summer and has signed a three-year contract, with Bayern's impressive appointment quashing the prospect of the former Barcelona boss moving to the Barclays Premier League in the near future.
Chelsea, last year's Champions League winners, have been repeatedly linked with the man Blues owner Roman Abramovich is reputed to admire greatly.
Reports have claimed he was offered a highly lucrative contract to take over at Stamford Bridge when interim manager Rafael Benitez's stint in charge finishes at the end of the season, and it has been confirmed that Guardiola turned down more money from elsewhere to go to Bayern.
Chelsea have never confirmed their interest in the former Spain midfielder, but his record at Barcelona, where he won 14 trophies in four years, made Guardiola the most sought-after out-of-work coach in world football.
It emerged that Guardiola signed up for Bayern before Christmas.
His agent Josep Maria Orobitg said: I don't know exactly which day, around the 20th or the second half of December."
Speaking on EFE Radio, Orobitg added: "He chose Bayern because of all the teams from which he had offers it was the best.
"We were looking over the offers and this isn't the team which offered the most money. It was chosen for the organisation there, for the potential that he sees, and for their players."
That raised the possibility that a Premier League club had offered big money to Guardiola, although AC Milan and wealthy Paris St Germain had also been credited with interest in him.
Orobitg added: "There have been things coming out from all sides that there had been offers, real meetings, false meetings, trips which didn't exist.
"From Christmas he had to choose his future. All this has been signed for some time. I didn't know that they were going to announce it this afternoon. In fact they informed me at 12 that it was coming out in a statement."
Since leaving Barcelona last summer, Guardiola has taken a career break and lived in New York, but now Bavaria and the Bundesliga beckons.
"I can imagine that he was overwhelmed by offers," said Franz Beckenbauer, the Bayern honorary president.
Beckenbauer told Germany's Sky Sport News HD: "I have to congratulate Bayern for bringing in Guardiola."
Former England midfielder Owen Hargreaves, who came through the Bayern ranks before joining Manchester United, believes moving to the Allianz Arena was an understandable step.
"Obviously Barcelona, Real Madrid and Manchester United are some of the biggest clubs in the world but Bayern Munich is easily among that top five," Hargreaves said on BBC Radio 5 Live.
"Bayern Munich is the Man United of Germany. They're both the biggest clubs in their countries. Germany is a bigger country than England and with 80 million people it is probably the healthiest league from an economic standpoint in all of Europe.
"I think all things considered it will be a great move for himself. He'll have a great team at his disposal, great resources and the fans are going to love to see what Bayern Munich have to offer in the coming season."
Bayern boasted Guardiola's signature will make the Bundesliga even stronger than at present, with its clubs making impressive progress in the Champions League.
Guardiola this week revealed his desire to one day coach in England, but he will be tied to Bayern through to June 2016, taking over from current boss Jupp Heynckes who at the age of 67 will retire in the summer.
Bayern chief executive Karl-Heinz Rummenigge said: "Pep Guardiola is one of the most successful coaches in the world and we are sure that he can make not just Bayern, but all of German football shine."
Guardiola will inevitably be linked with players from Barcelona but looks increasingly likely to take over a team of league champions at Bayern.
The retiring Heynckes is on course to lead Bayern to the Bundesliga title, with the team currently nine points clear at the summit. They are also in the last 16 of the Champions League and the quarter-finals of the DFB Pokal.
Heynckes first led Bayern from 1987 to 1991, claiming Bundesliga titles in 1989 and 1990, and returned on an interim basis in April 2009 to guide them into the Champions League qualification spots following the sacking of Jurgen Klinsmann.
Bayern chairman Uli Hoeness said: "As a worthy successor to Jupp Heynckes, only a coach of Pep Guardiola's calibre comes into question."
The appointment of Josep Guardiola came as a shock to former Chelsea manager Andre Villas-Boas.
Villas-Boas, now at Tottenham, told CNN World Sport: "I'm so surprised that I asked my media advisor from Tottenham if it was true. Obviously it's a big, big club, one of the biggest clubs in the world, in a league where we didn't maybe expect Guardiola to be in."
Borussia Dortmund managing director Hans-Joachim Watzke said: "I think it's great news.
"I can only congratulate Bayern wholeheartedly and without envy. It's a great story for the league, giving it even more of an international reputation.
"We need to respond to this but not right now, because Borussia Dortmund have the best coach in the world in Jurgen Klopp."