Spaniard Guardiola, 41, will take over from Heynckes, who has decided not to extend his contract, in July and has agreed a deal until the end of June 2016.
"We are very pleased that we have managed to convince the football expert Pep Guardiola, who was coveted and contacted by many top clubs, to come to Bayern Munich," Bayern CEO Karl-Heinz Rummenigge said on Wednesday.
"Pep Guardiola is one of the world's most successful coaches and we are sure that he can bring a great deal of sparkle not only to Bayern Munich but to German football in general," he added.
Bayern's announcement ended weeks of speculation about which club would win the race to hire Guardiola, who announced this month he would return to coaching next season after taking a year out to rest.
It is a significant coup for the German club, runners-up in Europe's elite club competition last season, given that big-spending rivals, including Chelsea, Manchester City and Paris St Germain, were reportedly also hoping to hire Guardiola.
"We can only congratulate Bayern for signing Pep Guardiola," said German football league (DFL) managing director Andreas Rettig.
"This shows the international standing of the Bundesliga and with Guardiola there will be even more interest in the Bundesliga."
Speaking to the English Football Association as part of the organisation's 150th anniversary celebrations this week, Guardiola had said his ambition was to manage in the Premier League.
Many credit Johan Cruyff, another former Barca player and coach, with creating the club's distinctive style and Guardiola played under the Dutchman in the 1990s when they won their first European Cup.
Whether Guardiola's philosophy and tactics will suit Bayern and the Bundesliga remains to be seen.
There is also a question mark over whether he can manage a group of players the majority of whom, unlike at Barca, did not come through the club's academy.
