We present the development of a low-noise, fundamental-mode, orthogonal fluxgate magnetometer with four amorphous, annealed ferromagnetic wires. The 1-Hz noise obtained in the open and closed loop is as low as 0.75 and 1.5 pT rms / $\surd $ Hz, respectively, with the white noise level about 0.6 pT rms / $\surd $ Hz. This is to the best of our knowledge the lowest figure published for a fluxgate magnetometer so far. By using the annealed sensor cores, we also found the offset drift to decrease approximately six times to 2.5 nT/K. We compared the instrument performance to a low-noise observatory magnetometer when doing geomagnetic measurements and show that it is fully suitable for measurements at mHz frequencies, e.g., magnetotellurics. The magnetometer performance enables room-temperature, unshielded magnetocardiography. With a gradiometric arrangement of two sensors, we were able to perform an MCG measurement in ambient field, and even without averaging, the signal could be clearly resolved.