"He is recovering normally at this point," said Dr. Craig R. Smith, the surgeon who led the four-hour operation. "I think right now everything looks straightforward."
Mr. Clinton, 58, was awake but sedated about four hours after the operation ended, said Dr. Allan Schwartz, chief of cardiology at New York Presbyterian Hospital/Columbia hospital. He still was using a breathing tube and had not spoken yet, he said.
Several of Mr. Clinton's arteries were more than 90 percent blocked, Schwartz said.
"There was a substantial likelihood that he would have had a substantial heart attack in the near future and that's the reason for the time emergency of what was done," he said.
In the bypass surgery doctors took arteries and a vein from his chest and leg, re-attached them to the main artery and also to a point below the blockage — "by-passing" the blockage and creating a new source of blood flow to the heart.
Mr. Clinton had to be placed on an artificial pump while his own heart was stopped for just over an hour, reports CBS News Medical Correspondent Elizabeth Kaledin.
Smith said Mr. Clinton could leave the hospital in four or five days. He said it takes two to three months for similar patients to fully recover.
Mr. Clinton has been at the New York hospital since Friday after suffering chest pains and shortness of breath and being told he would need to undergo heart bypass surgery as soon as possible. Mr. Clinton's tests showed no heart attack, but a source close to the family said there were three or four clogged arteries.
Asked whether there were any troubling moments during the surgery, Smith said: "There are always a few minor anxious moments during heart surgery. There was nothing in this case that was outside the realm of routine."
In a statement, Sen. Hillary Rodham Clinton and the couple's daughter, Chelsea, thanked the hospital staff for helping the family through an "emotional roller-coaster."
"The president's optimism and faith will carry him through the difficult weeks and months ahead," the statement said.
Schwartz said it would be possible for Mr. Clinton in the future to lead an "extraordinarily active lifestyle" — including hitting the campaign trail.
The former president's Web site said Mr. Clinton had received more than 30,000 get-well messages at his Web site e-mail address, including one which says: "I hope your doctors are good Democrats."
Mr. Clinton has also received a few fruit baskets, plus a call from Vice President Dick Cheney - who has had bypass surgery and several heart attacks - wishing him well.
Mr. Clinton, ever the loyal Democrat, reportedly also took time out for a 90-minute phone conversation with, giving the Democratic presidential candidate advice on how to win the election.
Mr. Clinton's medical problem is one faced by hundreds of thousands of Americans each year, especially those who smoke, are overweight, or have high blood pressure or high cholesterol.
Arteries get clogged by fat, which hardens into deposits that can cause a heart attack if they block one of the three main coronary arteries, each of which has one to three branches. Partial blockages can cause chest pain as the heart struggles to get by on less oxygen and nutrients than it needs.
Doctors sometimes do angioplasty, in which a balloon is inserted through a tube into a leg vessel and snaked to the blockage, where it is inflated to flatten the gunk against the artery wall, allowing blood to flow again. Tiny mesh scaffolds called stents may be placed to prop the vessel open.
But if the blockage is somewhere hard to reach or if many arteries are clogged, the best option may be bypass surgery, in which a vessel from elsewhere in the body is sewn in to detour blood around blockages.
More than 300,000 bypass surgeries are done every year, and according to Dr. Jeffrey Gold recovery depends on the individual. Mr. Clinton has a lot going for him given his "age and stamina and a vibrant drive such as he has."
"I predict that you'll get him wanting to be involved in things," Gold said. "There's a limit to how long he can watch the wallpaper in his home."
Still, Mr. Clinton's sudden onset of illness is a cautionary tale: He had heart disease in his family and a now legendary appetite for fast food. But he was also an avid jogger, took cholesterol-lowering drugs and had recently lost about 20 pounds.
It's a vivid reminder, says Gold, that heart disease takes decades to develop and never goes away:
"What the surgeons have done for him is they have turned the clock back. They haven't stopped it, and he will redevelop all these same problems over again if he doesn't watch his lifestyle," he said.