The pair were transferred to the Maryland hospital on the advice of the military. Military doctors strongly recommended they go to Bethesda because the hospital has the most expertise in handling the kinds of injuries they have suffered.
It is not known how long Woodruff and Vogt will remain at Bethesda.
Doctors at the Landstuhl Regional Medical Center in western Germany said they were surprised at how much the two had improved before their departure Tuesday.
Vogt was said to be awake, alert and talking.
"I asked him if he was ready to go to Bethesda," said Dr. Peter Sorini. "And he said he was from Paris and he preferred to go home. So I sort of sense that he had a bit of a sense of humor."
Woodruff has increasingly shown signs of consciousness.
"He started to wake up more -- move his arms and legs and just this morning started opening his eyes," said Sorini.
The two were taken to the Landstuhl late Sunday night after their convoy was hit by an improvised explosive device early Sunday near Taji, Iraq, about 12 miles north of Baghdad. Woodruff, Vogt and their four-man team were in the lead vehicle traveling in a convoy with Iraqi security forces. They were standing up in the back hatch of the vehicle taping a video log of the patrol at the time of the attack. Woodruff, Vogt and an Iraqi soldier were wounded in the attack.
Woodruff and Vogt suffered shrapnel wounds and underwent surgery at the U.S. military hospital in Balad. In addition to head injuries, Woodruff also suffered wounds to his upper body and broken bones.
Initial reports said the injured Iraqi soldier was "walking wounded," according to the American military. His current condition is not known.
Doctors say the immediate treatment Woodruff and Vogt received in Iraq, and the fact that both were wearing body armor, were crucial in their survival. They were also wearing helmets and ballistic glasses.
Woodruff and Vogt were taken by medevac to the Green Zone in Baghdad to receive treatment within 37 minutes of the blast. They were then flown by helicopter to Balad, which is about a 20-minute ride from Baghdad, said ABC News White House correspondent Martha Raddatz, who has covered the Pentagon and has extensive experience reporting from Iraq.
Woodruff said he believes his brother will want to get back to journalism as soon as he can.
"We want to see them recover and return to what he loves to do," he said. "Maybe not back to Iraq, but certainly I know he'll want to get back to what he's always wanted to do."
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. Woodruff has been on assignment in Iraq and planned to broadcast from the war-torn country this week for the State of the Union address.
A father of four, he was one of the first Western reporters in Pakistan following the Sept. 11 attacks.
Woodruff's overseas reporting of the fallout from Sept. 11 was part of ABC News' coverage that was awarded the Alfred I. DuPont Award and the George Foster Peabody Award, the two highest honors in broadcast journalism.
Woodruff has also covered the Iraq conflict in Baghdad, Najaf, Nassariya and Basra. During the initial invasion, Woodruff reported from the front lines as an embedded journalist with the First Marine Division, 1st Light Armored Reconnaissance Battalion.
Vogt, a 46-year-old father of three girls, has been with ABC News for more than 15 years and has extensive experience in war-torn regions. He was sitting next to ABC News producer David Kaplan when the producer was shot and killed in Bosnia. Earlier this month, he was with Woodruff in Iran and was recently in another convoy in which someone was killed by an IED.