We propose a new approach for the realization of very low noise programmable current sources mainly intended for application in the field of low frequency noise measurements. The design is based on a low noise Junction Field Effect Transistor (JFET) acting as a high impedance current source and programmability is obtained by resorting to a low noise, programmable floating voltage source that allows to set the sourced current at the desired value. The floating voltage source is obtained by exploiting the properties of a standard photovoltaic MOSFET driver. Proper filtering and a control network employing super-capacitors allow to reduce the low frequency output noise to that due to the low noise JFET down to frequencies as low as 100 mHz while allowing, at the same time, to set the desired current by means of a standard DA converter with an accuracy better than 1%. A prototype of the system capable of supplying currents from a few hundreds of μA up to a few mA demonstrates the effectiveness of the approach we propose. When delivering a DC current of about 2 mA, the power spectral density of the current fluctuations at the output is found to be less than 25 pA/√Hz at 100 mHz and less than 6 pA/√Hz for f > 1 Hz, resulting in an RMS noise in the bandwidth from 0.1 to 10 Hz of less than 14 pA.