The newsmen were flown Monday to the Landstuhl Regional Medical Center in western Germany.
"They're both very seriously injured, but stable," said Col. Bryan Gamble, commander of the Landstuhl facility. He said the two men were heavily sedated, and under the care of the hospital's trauma team.
Their body armor likely saved them, "otherwise these would have been fatal wounds," Gamble said.
Woodruff and Vogt, an award-winning cameraman, were embedded with the 4th Infantry Division and traveling in a convoy Sunday with U.S. and Iraqi troops near Taji, about 12 miles north of Baghdad.
They were wearing body armor and helmets but were standing up in the hatch of the mechanized vehicle when the device exploded, exposing them to shrapnel. An Iraqi solder also was hurt in the explosion.
"IED'S — improvised explosive devices — are the simplest — and deadliest — weapon in the insurgents' arsenal," reports CBS News correspondent Elizabeth Palmer. "They're basically homemade bombs, made of old artillery shells or stolen explosives, and hidden by the roadside."
"Doug was conscious, and I was able to reassure him we were getting them care. I spoke to Bob also and walked with them to the helicopter," said ABC senior producer Kate Felsen, who had been working with Woodruff for the past two weeks.
Woodruff, 44, assumed Jennings' old job anchoring "World News Tonight" with Elizabeth Vargas earlier this month.
"Bob and Doug were in Iraq doing what reporters do, trying to find out what's happening there up-close and firsthand. All of us are mindful of the risks and the dangers," Vargas said Sunday night in a closing note.
"Like countless civilians in the Iraq war, journalists are often casualties of the chaos," says CBS News correspondent Lara Logan. "It's increasingly the local media in Iraq who've paid the heaviest price: two out of every three journalists killed are Iraqi."
Dozens of journalists have been injured, killed or kidnapped in Iraq since the 2003 U.S.-led invasion that toppled Saddam Hussein.
My own close call came in Fallujah in 2004, during a routine patrol along an irrigation canal," says Palmer. "A buried shell detonated by a watching insurgent exploded. It was the gunner, exposed above the hatch in his vehicle, who took the force of the blast."
Woodruff and Vogt were riding in a similar position in their vehicle.
Logan also had a close call, two years ago in Afghanistan.
Jill Carroll, a freelance reporter for The Christian Science Monitor, was kidnapped by gunmen Jan. 7. She was among 250 foreigners who had been taken captive in the country since the U.S. invasion; at least 39 of those foreigners were killed.
The most visible among the U.S. TV reporters was David Bloom of NBC News, who died from an apparent blood clot while traveling south of Baghdad on April 6, 2003.
The Blooms and Woodruffs were known to be close friends, and when NBC News executives had to tell Bloom's widow that her husband had died, they made sure Woodruff's wife, Lee, was there to offer support.
The attacks on journalists bring constant media attention around the world to the insurgents, says Logan
Woodruff, a father of four, has been at ABC News since 1996. He grew up in Michigan and became a corporate lawyer in New York, but changed fields soon after a stint teaching law in Beijing in 1989 and helping CBS News during the chaos of the Tiananmen Square protest.
"Bob is a good man. He's not a hot dog. He prepares himself well. He doesn't take unnecessary risks," CBS News correspondent Byron Pitts said on CBS News' The Early Show. "But we all know once you step off the plane and get there, it's a dangerous place. And you can be as careful as humanly possible, but if it's your time, it's your time."
Vogt, 46, is a three-time Emmy award-winning cameraman from Canada who has spent the last 20 years based in Europe covering global events for CBC, BBC and now exclusively for ABC News. He lives in Aix-en-Provence, France.
ABC said that at the time of the attack both men were in an Iraqi vehicle — considered less secure than U.S. military equipment — to get the perspective of the Iraqi military. They were aware the Iraqi forces are the frequent targets of insurgent attacks, the network said.
Woodruff spent three days in Israel last week reporting on the Palestinian elections, and was to have been in Iraq through the State of the Union address on Tuesday, according to ABC.
ABC News' Jim Sciutto, who is covering the war in Iraq, said of Vogt: "He's the cameraman we all request when we go to the field because he's so good, a fantastic eye. He's won so many awards for ABC."
On CBS News' Face the Nation Sunday, anchor Bob Schieffer abandoned his commentary to wish Woodruff and Vogt well. "It just hit us all like a lightning bolt because we've all been there," he later said.
NBC "Nightly News" anchor Brian Williams said he had been in touch with Woodruff's family and is praying for the families of both men. "There is no way to cover the story in Iraq without exposure to danger," he said.