Bayern, who kick off their season later on Saturday in the Super Cup against RB Leipzig, said the 30-year-old striker was signed until 2027 after protracted talks between the two clubs.
The English club and Bayern had reportedly agreed on the move on Thursday but needed the consent of Kane, who has another year on his contract at Tottenham.
The 28-year-old needs five more goals to eclipse Rooney's mark of 53.
Harry Kane believes Tottenham Hotspur will have to win eight of their remaining nine Premier League games if they are to qualify for next season's Champions League.
Liverpool meets Tottenham Hotspur on Saturday night at the Wanda Metropolitano stadium in Spain to determine who will be UEFA Champions League title lifters.
In a tournament full of surprises, Gareth Southgate's young England team are the only former champions left in the lower half of the draw following the shock exit of Spain.
Mohamed Salah, Egyptian National Team and Liverpool's forward, was included by the Professional Footballer’s Association in the Premier League's Team of the Year.
The Professional Footballer’s Association has announced officially on Saturday the nominees for the Player of the Year award in England.
Mohamed el-Neny, Arsenal and Egyptian national team midfielder, announces that he voted for Mohamed Salah, Liverpool star, to be the Premier League Player of the Season.
Mohamed Salah, the Egyptian Liverpool star, won the Premier League Player of the Month Award from the Professional Footballers' Association (PFA).
Everton player Wayne Rooney believes that Harry Kane is likely to leave Tottenham if he does not win titles.
Tottenham Hotspur must replicate the form they displayed to outclass Manchester United in midweek if they are to get past an in-form Liverpool at Anfield in the Premier League on Sunday.
Mohamed Salah tops the list of the African scorers who play in the European leagues.
Harry Kane is on course to break all the goalscoring records in top-flight English football
Guardiola was named December's Premier League manager of the month, while Harry Kane equalled Steven Gerrard's tally with his sixth player of the month award
Harry Kane is happy to remain at the London club as long as they win silverware and provide him with the environment to improve as a player.
Harry Kane took his goal tally for the season in all competitions to 27 goals.
Harry Kane, widely known as "HurriKane", ended the 2017 calendar year as top scorer with 56 goals.
Harry Kane scored a Premier League record 37th goal in 2017 on Tuesday in Tottenham Hotspur's game against Southampton at Wembley Stadium.
Round 18 of the English Premier League will witness a strong match between Manchester City and Tottenham Hotspurs.