According to Sky Sports, the 21-year-old is already undergoing his medical in Scotland. The clubs are up against the clock, with the transfer window there closing on Thursday at 6pm German time.
The pay-TV broadcaster says the deal between the Swabians and the Scottish Premiership club is a loan with an option to buy. Slightly different figures are still doing the rounds over the exact financial terms.
While Bild report a fixed purchase option worth €18 million, kicker offer a more detailed breakdown: according to the specialist magazine, the Scots will pay a loan fee of around €500,000 to VfB and have secured an option to buy worth about €19 million.
That brings a transfer saga lasting several days to an end right at the deadline. Bouanani had already been waiting with packed suitcases on Tuesday, with a move to the Bundesliga on the cards.
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Which Bundesliga clubs were also interested in Stuttgart's Badredine Bouanani?
SV Werder Bremen held intensive talks with the Stuttgart club's management over a last-minute loan as they looked to bolster their attacking options. In the end, though, the parties could not reach an agreement.
Beyond Werder, other clubs also showed interest in signing the winger in recent days. FC Schalke 04 and French top-flight club Racing Strasbourg both looked into Bouanani.
Bouanani, a five-cap international who still had a contract in Stuttgart until 2023, only moved to the Neckar last summer. The Swabians paid a transfer fee of €15 million to OGC Nice. He made 28 competitive appearances for VfB, scoring two goals and providing two assists. But he played only 1,002 minutes and featured in coach Sebastian Hoeneß's starting line-up just 11 times.