He has served as United States ambassador to Malawi (2000–2003) and Democratic Republic of the Congo (2004–2007), as well as Charge d'affairs to Nigeria (2003) and to Ethiopia (2009).

Before joining the Foreign Service, Meece served extensively in Africa, beginning as a Peace Corps Volunteer in Sierra Leone in the early 1970s.

In Washington, Meece has served in the Bureau of International Narcotics Matters (1986–1988), on detail to the Office of the Vice President, and as Director for Central African Affairs (1998–2000) at the State Department.

Mostly notably, he played a central role in leading the international community efforts to help the Congolese government organize the free elections of 2006 in the Democratic Republic of Congo.

After his retirement from the U.S. State Department, Meece was appointed by the United Nations Secretary-General Ban Ki-moon as his Special Representative for the Democratic Republic of the Congo and Head of the United Nations Organization Stabilization Mission in the Democratic Republic of the Congo(MONUSCO) on 9 June 2010.