Gross-Selbeck, who was general manager of eBay Germany, will be responsible for further expansion of the Xing network and the continuous improvement of the range of services offered to its members.
He will begin his new role on January 15 next year.
Gross-Selbeck has worked in various managing positions for eBay. He has been responsible for the German business division since 2004 and supervised the company's growth.
During recent years, Germany became the biggest and most important eBay-market outside the U.S. and is today the eBay market with the highest reach worldwide.
Gross-Selbeck said: "I'm really looking forward to running such a dynamic and successful business.
"Xing is ideally positioned, and the structures for scalability of the business have already been created. I bring my particular experience in both B2B and B2C to help define the next phase of further corporate growth."
Hinrichs, the founder and current chief executive of Xing, will hand over his responsibilities to Gross-Selbeck during a brief transition phase.