"He will remain in the hospital for up to 48 hours to monitor his recovery. He is expected to resume a regular schedule when he is released to home," said Steve Schmidt, counselor to the vice president.
Cheney was scheduled to have only the right knee operated on Saturday, but his doctors decided to do both at once, Schmidt said.
An aneurysm is a ballooning weak spot in an artery that, as blood pounds through, eventually can burst if left untreated. The condition was discovered during Cheney's annual physical in July.
Cheney had flexible stents put in his knee arteries.
"Placement of the device in the right knee artery went exceedingly smoothly and an intra-operative decision was made to repair the aneuruysm behind the left knee using a similar technique," Schmidt said.
He said the surgery lasted six hours and there were no complications.
After the operation, Cheney was "awake, alert, comfortable," Schmidt said. The vice president was expected to be briefed on the impact of Hurricane Rita later Saturday.
The aneurysms, known as popliteal aneurysms, are not considered life-threatening.
Cheney, 64, has had four heart attacks, quadruple bypass surgery, two artery-clearing angioplasties and an operation to implant a special pacemaker in his chest. The pacemaker starts automatically if needed to regulate his heartbeat.
A vascular exam, part of a two-part annual physical Cheney completed in July, identified "small, dilated segments of the arteries behind both knees." But his overall cardio health was judged as good after the first part of the exam, which included a general physical exam, an electrocardiogram and a stress test.
The checkup determined that the pacemaker was working well and never had to be activated.