The first production Jazz Bass was made in March 1960 and listed at $279.50 for a sunburst-finish or $293.47 for blonde or custom-color finishes. The Precision bass had been around for nearly 10 years and Leo Fender decided that it was time for a new deluxe model. Compared to the Precision it was clear that the 1960 Jazz Bass was a deluxe instrument: it two pickups instead of one, giving it greater tonal versatility than the Precision.

When CBS bought the Fender companies in 1965 a number of minor changes were made to the Fender Jazz bass. During 1965  bound rosewood fingerboards with pearloid dot position inlays were introduced replacing the original clay inlays of the early 1960s. The machine heads were changed to oval shaped. Block-shaped fingerboard inlays and an optional maple fingerboard were introduced in 1966. At first necks with rosewood fretboards received pearloid blocks and binding and maple fretboard necks received black.

The Fender Jazz bass from 1975 to 1981 (CBS models) had a 3-bolt neck with bullet truss rod adjuster. These basses also had block fingerboard markers, with a white binding and block inlay option for maple fingerboards. The headstock logo was redesigned in 1976 and the serial number moved from neck plate to headstock logo. In 1977 the control knobs changed to black plastic with numbers.

The Fender Jazz bass had reverted to the 4 bolt neck and dot markers by 1983.

Mike Smith gave the following information on the 1983 Fender Jazz Bass: This bass also came with deluxe "F" tuning machines, Biflex tress rod, micro tilt neck and the pickups are located in the 70's Fender bass position. 1983 was the last year Fender manufactured the "Standard Jazz Bass" in the USA for a decade. And it was also the last year of the Fullerton built basses on the original equipment. Very few of these basses were produced in 1983 due to Fender building the new plant and being in the process of moving locations.