Allen, who has commanded the International Security Assistance Force and U.S. forces in Afghanistan since July 2011, will replace retiring U.S. Adm. James Stavridis. Allen is expected to take over his new role next spring, NATO said on its website.
The appointment, which was approved by the North Atlantic Council, followed Allen's nomination by President Barack Obama, which must be confirmed by the U.S. Senate.
NATO approval of the appointment was announced Wednesday during a meeting at the alliance's headquarters in Brussels.
"Gen. Allen has commanded ISAF through a very critical period. He oversaw the war at the height of its combat strength," U.S. Defense Secretary Leon Panetta said. "We have turned an important corner.
"If confirmed," Panetta added, "his experience as head of ISAF forces will be instrumental in leading NATO's oversight of the Afghanistan mission."
Allen will be replaced in Afghanistan by Marine Corps Gen. Joseph Dunford, the assistant Marine commandant, Stars and Stripes reported. Dunford, who served in Iraq but not in Afghanistan, will be responsible for overseeing the plan to end combat operations by the end of 2014.