Cheney is expected to remain in the hospital for up to 48 hours after Saturday's surgery at George Washington Hospital Center, said Lea Anne McBride.
The condition was discovered earlier this year during a routine checkup. The surgery will be performed under local anesthetic, his office said.
Cheney, 64, has had four heart attacks, though none since he became vice president in 2001. That year, he had an implantable cardioverter defibrillator inserted in his chest. The pacemaker starts automatically if needed to regulate his heartbeat.
An aneurysm is a ballooning weak spot in an artery that, as blood pounds through, can eventually burst if left untreated.
Typical surgical repair is to open the leg and sew a fabric patch onto the artery to reinforce the weak spot.
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.