"Age 801: Goku goes missing: realizing his death is imminent and wanting to settle their rivalry, Goku leaves the Earth with Vegeta for a final battle. Years later, a supernova explosion is detected; it is assumed to be from Goku and Vegeta's battle."
So Goku lives to about 64, being born in 737, and Vegeta to about 69. They presumably realized their bodies didn't have much time left, which means Saiyans have comparable lifespans to humans.
They will live longer than Earthlings, but not by much. They just wanted to go off and have a final battle so that they could die a Saiyan's death; on the battle field, instead of getting old and not being able to maintain their power. Once Saiyans reach a certain age (probably different for each one), they rapidly age into a more fragile state.
Also, Vegeta lives to physically be 71 (two years in the RoSaT), while Goku is only physically about 57 (8 years dead, one year in RoSaT).