The men were airlifted to the Landstuhl Regional Medical Center in western Germany after their convoy was hit by a roadside bomb early Sunday near Taji, north of Baghdad. An Iraqi soldier was also wounded in the attack.
They suffered shrapnel wounds and underwent surgery at the U.S. military hospital in Balad, and were then headed Bethesda (Md.) Naval Hospital for further treatment, the network said.
"They couldn't ask for better stats at this time," doctors in Germany said. "The signs are good and we are very optimistic."
Doctors said the immediate treatment they received in Iraq, and the fact that both were wearing body armor, helmets and ballistic glasses, were crucial in their survival.
Along with Elizabeth Vargas, Woodruff, 44, was named co-anchor of "World News Tonight" last month, replacing Peter Jennings, who died of lung cancer last year.