SC Paderborn officially announced on Thursday that the 22-year-old is joining reigning Scottish champions Celtic Glasgow.
"We would actually have very much liked to keep him," said Paderborn sporting managing director Sebastian Lange. "When he expressed his wish, we did not want to stand in his way in view of there being less than a year left on his contract, on the condition that our SCP also benefit from it."
Sky had previously reported that an agreement was close. Baur is said to have signed a contract with the Premiership club until 30 June 2031.
Mika Baur becomes SC Paderborn's record sale
Lange called it a "very good economic solution", which the Bundesliga club will use "to further strengthen our squad until the end of the transfer window".
The fee is said to be eight million euros, which would make it a new sales record for Paderborn. Aaron Zehnter had held the previous mark after the 21-year-old joined VfL Wolfsburg a year ago for 4.5 million euros.
