A technique for measuring ultra-low electric currents from living cells, using electrodes, biosensors or magnetic detectors is reported, based on the design of a sensitive, ultra-low-noise trans-impedance amplifier. This technique offers a low-noise, low current measurement capability down on the order of 2 x 10-14 amperes, with specifications such as input leakage current of less than 1 x 10-15 amperes and a dynamic range of 30-100 x 10-14 amperes. Maximum bandwidth of roughly 1KHz was observed, while working in the specified dynamic range. This set of specifications is quite satisfactory and desirable for many low-frequency applications in bioelectromagnetism and bio-amperometry. The technique finds numerous applications in studying intrinsic cellular fields and induced currents originated in cells under physiological conditions. A few applications envisaged for its possible utility include bio-sensing amperometry, general studies in bioelectromagnetism and ion transport studies in plasma membrane and mitochondrial inner membrane, by incorporation of the amplifier with suitable micro-electrodes or nano-scale electrical, magnetic or optical sensors.