Murray will take on the role as of 1 September and will continue to report directly to chief executive and president Rudi Lenz.
Lenz said: "During his tenure in Europe, Charles has dealt with the varying challenges impacting our industry successfully and has shown himself at all times to be a tenacious and strong leader.
"I have no doubt that he will make an invaluable and immediate contribution to the future growth of Sun Chemical's North American Inks business."
In the interim, Sun Chemical's UK, Ireland and Nordic business will be led by Gerry Brady, the company's chief financial officer, until a successor is announced.
Sun Chemical produces printing inks and pigments for the packaging, publication, coatings, plastics, cosmetics markets.