Grube, aerospace and defense company EADS's Non-Executive Chairman, had said on Tuesday he would step down to run Germany's rail operator.
He had been nominated for that post last week after the resignation of Hartmut Mehdorn who succumbed to mounting pressure over revelations that Deutsche Bahn
On April 30, Grube will leave the management board of Daimler, the German carmaker that holds a 22.5 percent stake in EADS, to start his new job at Deutsche Bahn.
EADS is controlled by Daimler and a French entity comprising media group Lagardere
At 0954 GMT shares of EADS were down 0.9 percent at 9.49 euros, while Daimler's stock was up 3.7 percent.
(Reporting by Maria Sheahan; Editing by Hans Peters)