In this paper an approach for designing a programmable, very low noise, high accuracy voltage source for biasing devices under test in low frequency noise measurements is proposed. The core of the system is a supercapacitor based two pole low pass filter used for filtering out the noise produced by a standard DA converter down to 100 mHz with an attenuation in excess of 40 dB. The high leakage current of the supercapacitors, however, introduces large DC errors that need to be compensated in order to obtain high accuracy as well as very low output noise. To this end, a proper circuit topology has been developed that allows to considerably reduce the effect of the supercapacitor leakage current on the DC response of the system while maintaining a very low level of output noise. With a proper design an output noise as low as the equivalent input voltage noise of the OP27 operational amplifier, used as the output buffer of the system, can be obtained with DC accuracies better that 0.05% up to the maximum output of 8 V. The expected performances of the proposed voltage source have been confirmed both by means of SPICE simulations and by means of measurements on actual prototypes. Turn on and stabilization times for the system are of the order of a few hundred seconds. These times are fully compatible with noise measurements down to 100 mHz, since measurement times of the order of several tens of minutes are required in any case in order to reduce the statistical error in the measured spectra down to an acceptable level.