After two years with Manchester United, Kagawa re-signed for BVB last week in a deal worth £.6.3 million.
The Japan international is regarded as a genuine star inside German football and Rummenigge says the Bundesliga will be stronger for his return.
"Every transfer to the Premier League is a shame - and this was one without question - so we should welcome him back," said Rummenigge.
"We need a big competition and emotionality in the Bundesliga. Each well-known player is welcome."
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