Natsios had overseen a push to end violence, which the US calls genocide, in the western Darfur region.
He also worked to maintain a 2005 peace agreement that ended decades of civil war between north and south Sudan.
After news of the resignation became public, Darfur advocates called for the White House to appoint a full-time envoy to deal with the crisis which has killed more than 200,000 people and displaced more than 2.5 million since 2003.
"The president should appoint a full-time envoy answering directly to him, and end the crippling turf battles once and for all," said John Prendergast, co-chair of the ENOUGH project and a board member of the Save Darfur Coalition.
Prendergast said Williamson, Natsios's replacement, is a "hard-nosed negotiator" who cares deeply about the plight of the Sudanese people and might be more able than Natsios to break through the bureaucracy to make a mark on Sudan policy.
Williamson is a senior Republican party official who has in the past worked closely with John Negroponte, now Deputy Secretary of State.
Natsios plans to return to a full time teaching position at Georgetown University.