In this work we report on the measurement, with record accuracy, of the absolute modal effective refraction index (phase index) of single mode optical fibers by using Bragg gratings. We also demonstrate a new method to measure the group index of the fibers from the gratings Bragg wavelength. We present as well the characterization of the thermo-optic and strain-optic coefficients as a function of the wavelength, the values we have obtained are the closest to those of the pristine fiber measured with gratings technology so far. The phase index is measured with a set of gratings in the wavelength range from 1509 nm to 1563 nm and the group index is obtained from the wavelength dependence of the phase index. Very weak gratings with reflectivity down to 10-3 have been used in order to minimize the perturbation of the pristine fiber. Results are presented at a temperature of 22°C and zero strain after preliminary calibration of the thermo-optic and strain-optic coefficients as a function of the wavelength. Accuracies better than 3×10-5 and 7×10-4 have been achieved for the phase and group indices, respectively. It is also shown that the main source of error relates to the uncertainty in pitch of the phase masks used for gratings inscription. The technique is useful for testing different kinds of fibers including telecommunication, amplifying, and polarization maintaining.