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Sommer made 94 appearances for his country since making his debut in 2012.
Xabi Alonso's team, who have now gone a league-record 29 matches without defeat this season to secure their first trophy since 1993, have a 16-point lead over Bayern with five matches remaining.
Bayern CEO Jan-Christian Dreesen said there would a 'a new direction' next season with a new coach.
The attacking full-back and dead-ball specialist became an instant Germany football great when his spot-kick earned them a 1-0 victory over Diego Maradona's Argentina in the World Cup final in Rome in 1990.
England captain Kane, who joined for a league record 100 million euros last week to solve Bayern's scoring problems, slotted their second goal in the 74th minute after setting up Leroy Sane for a fourth-minute opener.
Despite a stellar scoring record he failed to win any domestic or international titles with Spurs.
Bayern did not disclose the transfer fee, which media reports have put at around 100 million euros ($109 million). That would be a Bundesliga record.
Should it be completed, Kane's move would be the most expensive transfer in Bundesliga history with an expected fee of about 100 million euros.
Medical examinations showed the 30-year-old right-back has lymphoma and he will now have several months of treatment.
Borussia Dortmund needed a win to lift the title but ended up drawing 2-2 with Mainz.