Naess, 24, leaves Columbus for the Eredivisie after a year in MLS, having made 31 league appearances. A center back and defensive midfielder, Naess joined the Crew from Norwegian side Stabaek in July 2016.
Per MLS policy, details of the deal were not disclosed.
"Nico is a talented young player with a great character and a bright future. We are happy to reach an agreement with SC Heerenveen that benefits both Nico and our club," Columbus coach and sporting director Gregg Berhalter said in a news release.
"As a club, we take pride in developing the international and professional careers of players on our roster. Nico worked hard for this opportunity and we wish him well in the next step in his career."
Naess' exit leaves Jonathan Mensah, Josh Williams, Alex Crognale and Lalas Abubakar as the center backs on Columbus' roster.