Bayern Munich striker Harry Kane arrived in Germany on a record-breaking transfer and his sensational goal-scoring run this season has already exceeded expectations and turned him into an instant fan favourite.

Kane joined Bayern from Tottenham in August for a Bundesliga-record 100 million ($106m) fee, with the German champions desperate to bring in a tested scorer to fill the goal-scoring gap created by last year's departure of Robert Lewandowski to Barcelona.

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Kane, the England men's all-time top scorer and the Premier League's second all-time scorer, hit the ground running and has already bagged 21 goals in 15 matches in the Bundesliga and Champions League for Bayern.

"It is impressive," beamed Bayern sports director Christoph Freund after Saturday's double in their 4-2 victory over Heidenheim.

"He is playing away from the U.K. for the first time and then he scores like that. The team also plays him into position. He is a phenomenon."

Kane's two goals on Saturday took his league tally to 17 from 11 games, setting a league record for most goals at this stage, beating Lewandowski's previous mark of 16.

Kane already has more goals after 11 Bundesliga matches than last season's top scorers had in the entire campaign.

"I cannot tell you anything different," Bayern coach Thomas Tuchel said of Kane's scoring run on Saturday. "The performances are telling a story. There is no need for any words."

Kane has also scored four times in four Champions League group matches, with Bayern having already secured a spot in the knockout stage with two games to spare.

Among the highlights this season is his 60-metre looping shot from Bayern's own half in their 8-0 demolition of Darmstadt 98, undoubtedly a candidate for goal of the season.

He also scored a hat trick in last week's 4-0 victory at title rivals Borussia Dortmund, the first player to do so in their Klassiker debut.

"I believe he can do anything," said Bayern teammate Thomas Müller. "We only need to bring him into position. If he gets to shoot anywhere near or inside the box then chances are the ball will go in."

Club bosses are equally delighted with Kane's goal bonanza, saying the move was the right one for both Bayern and the title-starved Kane.

"Absolutely fantastic," Bayern CEO Jan-Christian Dreesen said. "Obviously one is happy when things are working so well, having also been partly responsible for this transfer. I hope it continues like that."

Kane's scoring exploits have also forced some critics of the transfer to make a sharp U-turn. Among them is former Germany international Didi Hamann who had initially expressed doubts about how effective Kane would be in the Bundesliga.

"I never thought that he would score like that," Hamann told Bild newspaper. "I mean he did not sign for three months but for four years and he gets great balls from team mates."

"But still it is impressive because he is one of a few strikers who don't have so much speed. But it shows you how clever he is as a player. Bayern did everything right. He is a phenomenon."