Woodruff and Vogt were flown to Andrews Air Force Base in Maryland, on a military plane from Germany. The two men were to be taken to the brain injury center of the National Naval Medical Center in Bethesda, Md.
Woodruff's brother said the "World News Tonight" co-anchor's condition "improved markedly" overnight, and a doctor said the prognosis for both injured men was "excellent."
A C-17 medical evacuation plane took off from the U.S. base at Ramstein on Tuesday afternoon carrying the two journalists and 28 U.S. service personnel, including several others hurt in Iraq.
Members of the 86th Air Medical Evacuation Squadron, based in Ramstein, would tend to the patients in the air, U.S. military spokeswoman Erin Zagursky said. Relatives of the men were traveling home on commercial flights, she said.
David Woodruff told ABC's "Good Morning America" on Tuesday that his brother's condition "improved markedly over the night. He looks much better than he looked the day before."
"His signs are great, probably as good as can be expected at this stage," he said. "We're all so encouraged."
A neurosurgeon at military hospital said Woodruff, who suffered head injuries and broken bones, again moved his arms and legs and opened his eyes Tuesday morning.
"He's making progress," Col. Pete Sorini said. "I believe Doug's and Bob's prognosis is excellent."
Doctors in Maryland will try to take Bob Woodruff off a breathing machine, Sorini said.
ABC News President David Westin issued a statement Tuesday saying Vogt was talking with others but Bob Woodruff "continues to be heavily sedated and may be for a time."
"It will still likely be some time before we have a complete sense of the injuries, but with each day there are promising signs," Westin said. "As before, we have a very long way to go."
"Doctors will purposely keep his pressure in his brain under control by heavily sedating him so as not to raise the pressure and make the swelling worse," Dr. Maurizio Miglietta, chief of trauma and critical care at the New York University School of Medicine/Bellevue, tells CBS News' The Early Show co-anchor Harry Smith.
The two men were brought to the airport in a gray bus and carried onto the plane on stretchers. Both were wrapped in blankets and attached to life-support machines.
Bob Woodruff and Vogt were taken to the nearby Landstuhl Regional Medical Center on Monday. Medics there said the pair were showing signs of improvement from serious injuries inflicted in a roadside bombing.
Bob Woodruff, who was most seriously hurt, briefly opened his eyes Monday and responded to stimuli to his hands and feet, ABC said earlier.
Col. Bryan Gamble, the commander of the hospital, described Bob Woodruff and Vogt as "very seriously injured, but stable" with injuries "typical of victims of improvised explosive devices."
Woodruff, 44, and Vogt, a 46-year-old award-winning cameraman, were embedded with the 4th Infantry Division and traveling in a convoy with U.S. and Iraqi troops near Taji, about 12 miles north of Baghdad when the device exploded, reports CBS News correspondent Byron Pitts. They were standing in a rear hatch – exposed – videotaping a report when the attack happened Sunday.
David Woodruff said his brother fell down the hatch after the blast, opened his eyes and asked if he was alive.
"At that point he started to feel the pain, I think, and he used some colorful language and said, 'This hurts a lot.' And then he became unconscious," he told "Good Morning America."
"I think he knew he knew he was in danger, but at the same time, he really wanted to get the news and wanted to get it right," Woodruff's other brother, James, told CBS News. "And sometimes when you need to get it right, you need to put yourself right up there."