The stents - wire-mesh tubes that help the flow of blood - were placed in a coronary artery that had become blocked since Mr Clinton had a quadruple-bypass operation in 2004.
Speaking to media outside the Columbia Campus of New York Presbyterian Hospital on Thursday evening, Dr Schwartz said the former president had been feeling discomfort in his chest for several days.
"Of the four bypass grafts that he had six years ago, one of the bypass grafts was completely blocked," the cardiologist said.
HOW A CORONARY STENT WORKS
1. The stent is a wire mesh tube used to hold open narrow arteries. It is guided into place by a catheter
2. Once in position the catheter is inflated and the stent is expanded
3. The catheter is removed and the stent remains in place to help keep blood flowing through the artery
"The artery that had been supplied previously by this bypass graft was opened by placing the two stents."
He added: "President Clinton has since been up and walking around and visiting with his family. He is in good spirits."
The BBC's Steve Kingstone in Washington says it is being stressed that Mr Clinton's diet and active lifestyle were not triggers for this scare.
The former Arkansas governor became known for his love of fast food and jogging during his two terms as president.
He later set up the William J Clinton Foundation to promote and address international humanitarian causes such as treatment and prevention of HIV/Aids and global warming.
Last year, he was appointed UN special envoy to Haiti, where he has been working in recent weeks to help the relief effort in the wake of the devastating earthquake there on 12 January.
The White House said Mr Clinton had told President Barack Obama he felt "absolutely great" after the procedure.
"[Mr Clinton] said that the efforts in Haiti were too important for him to be laid up for too long and hopes he'll be ready to get back to work as soon as possible," the White House said in a statement.
Born on 19 August 1946 in Hope, Arkansas
Elected Democratic governor of Arkansas in 1978
Becomes US president in 1993, defeating George Bush Sr
Re-elected president in 1996, beating Bob Dole
Cleared of all charges in his impeachment trial over Monica Lewinsky sex scandal in 1999
Launches William J Clinton Foundation after stepping down as president in 2001
Appointed UN special envoy to Haiti in 2009
A friend of Mr Clinton told ABC News that he had been suffering from a cold and had been worn out from a trip to Haiti last week.
Stents are used to keep an artery open after it is unclogged in the angioplasty.
Doctors thread a tube through a blood vessel in the groin to a blocked artery, inflate a balloon to flatten the clog, and slide the stent into place.
One of the most common medical procedures worldwide, more than a million angioplasties are carried out in the US alone each year.
Dr Clyde Yancy, the president of the American Heart Association, said it was "not unexpected" that Mr Clinton needed new stents.
Patients often required another procedure five to 10 years after a bypass or angioplasty because new clogs tended to develop, he said.
"This kind of disease is progressive. It's not a one-time event, so it really points out the need for constant surveillance," Dr Yancy told the Associated Press.
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