Neumann, who has revamped Opel's image since taking charge of the troubled carmaker in March 2013, will be succeeded by finance chief Michael Lohscheller, Opel said.
"Under Neumann's leadership we have made enormous progress in turning around Opel," GM President Dan Ammann said in an emailed statement. GM's European operations also include the Vauxhall brand.
Neumann, 56, previously ran Volkswagen's operations in China and, in former roles, was in charge of VW's electric-car business and chief executive of German auto parts and tyre maker Continental <CONG.DE>.
VW is looking at rehiring Neumann, possibly to lead its Audi luxury brand, where chief executive Rupert Stadler has come under fire, a source told Reuters on Sunday.
Neumann said on Twitter he will stay as member of Opel's management board until the closing of the acquisition by PSA.