As revealed by Sources earlier this week, the 44-year-old Spaniard will leave the Bundesliga giants and is expected to take over at Manchester City.
Guardiola, who has won back-to-back league titles in Germany since taking up the reins at the Allianz Arena, has decided to embark on a fresh challenge.
Rummenigge said of Guardiola’s decision to leave the club: ‘We are thankful to Guardiola for all he gave our club and hope to celebrate more success in the current season.
‘With Ancelotti we have another very successful coach coming to Bayern. We are looking forward to working together.’
Manchester City have been linked with Guardiola over the past few seasons and could finally land the former Barcelona boss at the end of the current campaign if they decide to replace Manuel Pellegrini.
The current City boss has openly admitted Guardiola and Manchester City would be a good fit if he was to replace him at the Etihad Stadium.
‘I cannot talk about Pep because I am not Pep but what I can say is that I’m sure important managers always want to work here in the Premier League,’ said the Manchester City manager ahead of his game at Arsenal on Monday night.
‘Pep Guardiola will work here, I don’t know if it is next season here or at another club, I am not sure. Some day he will come here.
‘I hope he will have the option to work at Manchester City because I love this club and I hope in the future he can do it also as I am sure that he will be very important for the club also.
‘That is a lot of things that will happen in the future! When is the future? You never know. But if the future is next year, the only thing I am worried about is this year trying to win the most amount of titles I can and not worry about the other things.’
Ancelotti, who has agreed a three-year deal with Bayern, is currently enjoying a year-long sabbatical following his departure from Real Madrid in May 2015.
The Italian said ahead of his move to Bayern: ‘It’s an honour for me to be a part of this great club next season, FC Bayern Munich.
‘When I knew of the club’s interest I didn’t want to consider any other offer.
‘I honestly wish FC Bayern Munich and my friend Pep Guardiola the best for the current season.
‘I wish a merry and peaceful Christmas and a happy new year to all Bayern fans and to all of you.’
He posted the message in English, Spanish, Italian and German following news of his appointment.
His former right-hand man Paul Clement, now manager of Derby, tweeted: ‘Great news Coach! @MrAncelotti congratulations.’
Bayern have moved quickly to appoint Ancelotti following Guardiola’s refusal to put pen to paper on a contract extension.