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.