Doctors said Kennedy was awake for much of the three and a half hour surgery.
Kennedy is only surviving brother of John F Kennedy, the US president who was assassinated on November 22, 1963 in Dallas, Texas.
His brother Robert Kennedy was also assassinated in 1968, shortly after he announced his bid for the US presidency.
The eldest brother, Joseph Patrick Kennedy, was killed in World War II.
Kennedy was diagnosed last month with a malignant glioma, an often lethal type of brain tumour.
Cutting a tumour down to size is especially delicate because of the risk of harming healthy brain tissue that governs movement and speech.
But Friedman, the top neurosurgeon at Duke and an internationally known tumour and vascular surgeon, said Kennedy should not experience any permanent neurological effects.