Mr Cheney, 64, returned to his official residence four and a half hours after being rushed to the George Washington hospital.
Mr Bush played down fears over the health of his number two, who is regarded as one of the most powerful men in the US.
"He's doing fine. I talked to him this morning. His health is good," Mr Bush told reporters during a trip to a school in the Washington suburbs. "He'll be coming in to work a little later on today."
Asked whether Mr Cheney's health would allow him to finish the last three years of the Bush administration, White House spokesman Scott McClellan told reporters: "Absolutely."
Mr Cheney "is a very important member of the team," Mr McClellan said.
The vice president has suffered several heart attacks over the past 25 years.
Aides said Mr Cheney was admitted this time for treatment after retaining fluid in connection with medication he was taking for a foot problem.
"The vice president, experiencing shortness of breath, went to George Washington Hospital at 3:00 am this morning," another Cheney spokeswoman, Lee Ann McBride, said.
"His doctors found that his EKG (electrocardiogram) was unchanged and determined that he was retaining fluid as a result of anti-inflammatory medication he has been taking for a foot problem. They have placed him on a diuretic," Ms McBride added.
In September, Mr Cheney underwent surgery to remove blood clots behind each of his knees.
He underwent the surgery after doctors found an aneurysm behind his right knee during a routine check-up, his office said.
No problems with the left knee were mentioned at the time. Left untreated, such an aneurysm could lead to amputation.
In November, Cheney was tested at the same hospital after experiencing shortness of breath, but released when no major problems were found.
Mr Cheney underwent angioplasty in November 2000 after suffering his fourth heart attack since 1978. He had a cardioverter defibrillator implanted in June 2001 to regulate his heartbeat.
The device, implanted just beneath Cheney's left collarbone, can administer electric shocks to slow a potentially dangerous racing heartbeat or speed up an excessively slow one.
Last week, he appeared at a Harley-Davidson manufacturing plant in Missouri, where he made a speech on the economy, holding a cane.
He joked that he did not "ordinarily carry a cane like that, but (Defense Secretary) Don Rumsfeld has been chewing on my ankles."
Mr Cheney is considered one of the most powerful vice presidents in US history and one of the architects of the Iraq war.
He was defence secretary during the 1991 Gulf War and it was a surprise when he teamed up with George W Bush for the 2000 election.
The Bush-Cheney team was re-elected for a second four year term in November 2004.
He is fiercely loyal to Mr Bush and insists he has no presidential ambitions of his own.