"Filip Kostic has arrived at Caselle airport for his medical visit at Juve," the club reported.
According to Italian newspaper Gazzetta dello Sport reports, Frankfurt will receive around 15 million euros, which could rise as high as 17 million euros with bonuses, for the 29-year-old Serbian international.
Kostic was crucial in Frankfurt’s unlikely run to the Europa League title in 2021-22, which saw him named Europa League player of the season.
The Serbian’s performances had led to speculation he may leave Frankfurt in the summer, with Italy the likely destination.
His exit became clear on Tuesday, when it emerged he had not travelled with the team to Helsinki for their UEFA Super Cup clash with Real Madrid.
Frankfurt manager Oliver Glasner has lamented the loss of his star winger who was under contract until 2023, but said he leaves as a "hero".
“From a sporting point of view, this leaves us weaker,” the Austrian coach said on Tuesday.
"One of my eyes is smiling and one is crying. It is clear he has left his mark."
Eintracht goalkeeper Kevin Trapp said Kostic had "made history with us".
At Juventus, Kostic is linking up with his Serbian compatriot Dusan Vlahovic who arrived at the club in January, with the pair also set to figure in the World Cup finals where Serbia face Brazil, Cameroon and Switzerland.
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