Cheney left Inova Fairfax Heart and Vascular Institute in Northern Virginia to continue his recovery at his home, according to a statement released by his office.
Cheney, 69, has had five heart attacks since he was 37 and suffers from congestive heart failure. He disclosed in a statement on July 14 that he had undergone surgery the previous week after what he called "entering a new phase of the disease when I began to experience increasing congestive heart failure."
Congestive heart failure - the heart weakens and cannot pump blood as needed - affects about 5 million Americans.
Cheney said at the time that the pump, called a left ventricular assist device, would allow him to resume an active life. His daughter Liz said last week that the former vice president has been planning trips to fly fish and hunt.
The battery-powered pump is mainly used for short periods by a heart transplant candidate awaiting a donor organ. Such devices are being studied for use by people with severe heart failure who aren't candidates for transplants. The pump relieves pressure on the heart by rerouting blood.
Cheney said last month that he chose the surgical procedure after testing and consultation with doctors.
"He and his family express their gratitude for the tremendous care he has received from the medical staff at Inova Fairfax and at George Washington University Hospital," the statement on Monday said. "They also want to thank the many people who have reached out with letters and prayers and warm wishes."