Mukiele appeared destined to become a PSG player when Leipzig announced he had been granted absence from its squad for the DFL-Supercup due to ongoing transfer negotiations on Tuesday.
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Despite reports of late interest from Chelsea, PSG sealed the acquisition of the 24-year-old and will reportedly pay an initial €12million fee, which could reach a total of €16million with add-ons included.
Mukiele has signed a five-year deal at the Parc des Princes, becoming the third new arrival of the transfer window after midfielder Vitinha and striker Hugo Ekitike, while left-back Nuno Mendes made his loan from Sporting CP permanent.
Speaking to PSG's website, Mukiele said: "When I found out that Paris were interested in me and that they wanted me to come here, I had to think about it because it's very important.
"It's a very big step in my career, it's not a choice to be taken lightly. But I think and I'm sure I made the right choice."
Mukiele made 28 appearances – 21 of them starts – as Leipzig finished fourth in the Bundesliga last season, contributing to the side matching Bayern Munich as the competition's best defensive side.
No Bundesliga team conceded fewer than their 37 goals across the 2021-22 campaign, while only Bayern and Wolfsburg (both 11) bettered their tally of 10 clean sheets.
PSG won three out of three fixtures during a pre-season tour of Japan, though Galtier expressed frustration with its defending after Tuesday's 6-2 rout of Gamba Osaka.
Mukiele, who is capable of playing at full-back and centre-back, is expected to challenge for a spot in a three-man backline next season.