Schurrle, who is understood to have agreed personal terms with the Blues, is on international duty for Germany in the USA and will likely head straight to London to finalise the deal following his release from the national team.
The 22-year-old is set to join the Europa League winners in a reported £20 million deal that will see Belgium international Kevin de Bruyne move in the opposite direction on loan.
"We have reached an agreement with Chelsea," Wolfgang Holzhauser told the Rheinische Post newspaper.
"They are going to buy Andre Schurrle for a specific fee and, in return, they will loan De Bruyne to us for a year for free.
"I expect Chelsea to stand by what has been agreed."
De Bruyne's involvement was key to the agreement being struck, but speculation linking the player with Champions League runners-up Borussia Dortmund had thrown the deal into doubt.