Vogt and his wife, Vivian, are on their way home to France, where he will undergo further treatment.
In a statement, ABC News President David Westin described the couple as being "in good spirits and looking forward to getting back to their children."
The more seriously hurt Woodruff, recovering from head wounds and other injuries at the National Naval Medical Center in Bethesda, Md., is being slowly brought out of sedation, Westin said.
"Despite the fact that he continues to be mildly sedated, Bob has been out of bed in a chair and his physical strength continues to impress his entire team," Westin said. "We've come some distance, but we still have a long way to go."
Westin added that "in another sign of Bob's moving along his path to recovery," his doctors have said that in the next few weeks he might move to facilities near his home in the New York area.
Charles Gibson and Diane Sawyer are currently subbing for Woodruff, co-anchor of ABC's "World News Tonight" with Elizabeth Vargas.