The Chilean had previously been heavily linked with a move to French club Marseille but a deal could not be reached.
According to sportmediaset.it, the deal is all but done and only needs to be made official as the 26-year-old has already passed a medical with the German club.
The transfer fee is a reported €5 million plus an additional percentage of any future sell-on fee that the German side may receive for Vargas.
Vargas has had little playing at Napoli since moving from Universidad de Chile for $18 million.
He was subsequently shipped out on loan to Gremio, Valencia and Queens Park Rangers before returning to the Stadio San Paolo this summer after he was part of his country’s Copa America victory.
Vargas will become the second striker to leave Napoli along with Duvan Zapata who has joined Udinese on loan as new coach Maurizio Sarri restructures the team.