We report on the design of an n-channel Junction Field Effect Transistor (JFET) on fully-depleted, high-resistivity (5 kΩ cm), n-type silicon substrate, which is intended to be utilized as an active device in the on-chip preamplifier of the silicon radiation detectors we are developing. Two-dimensional process and device simulations are employed to optimize the device doping profile, as well as to point out some important advantages of the proposed structure over possible alternative device designs. In particular, the proposed JFET, in which an externally-contacted, p-type well isolates the active device from the high-resistivity substrate, presents higher output-resistance values than a device directly fabricated on substrate. Moreover, it is not affected by a parasitic phenomenon resulting in gate-current increase and noise-performance degradation, which, in contrast, characterizes a device with a floating well.