De Nysschen, who was based at Infiniti's global headquarters in Hong Kong, will leave the company at the end of this month. He'll take up presidency at Cadillac at the beginning of August, reporting directly to GM boss Dan Ammann.
In the meantime it is expected that Nissan boss Andy Palmer will take over at Infiniti until a successor is found.
Figures released earlier this week show that Infiniti sold a total of 101,200 new cars globally in the first six months of 2014 - a new record.
The brand is currently gearing up to begin production of new models - including a long-wheelbase version of the Q70 saloon - in China, with the aim of cementing the brand's position in the world's largest car market. The first locally built Infiniti models are due to roll off the line in 2017.
According to a leaked dealer presentation this month, other models set to launch in China for the brand include the Q50, QX60 Hybrid and a sportier version of the QX70. Also on the list is a rebadged version of the Nissan Juke Nismo - which will be sold with the name ESQ - and a facelifted QX50L.
The leaked plan also reveals the brand's plans to grow its China dealer network, opening up small franchises in cities across the country to boost sales.
Speaking about his appointment at Cadillac, de Nysschen said: "I have for some time now been impressed by how the new General Motors has been transformed into a formidable force in the industry.
"The combination of strong corporate leadership and exceptional engineering resources presents the perfect combination to restore Cadillac to its place among global premium brands."
Get the latest car news, reviews and galleries from Autocar direct to your inbox every week. Enter your email address below: