We present measurements of the Faraday and the Cotton-Mouton effects of helium gas at $\lambda~=~1064$\,nm. Our apparatus is based on an up-to-date resonant optical cavity coupled to longitudinal and transverse magnetic fields. This cavity increases the signal to be measured by more than a factor of 270\,000 compared to the one acquired after a single path of light in the magnetic field region. We have reached a precision of a few percent both for Faraday effect and Cotton-Mouton effect. Our measurements give for the first time the experimental value of the Faraday effect at $\lambda$=\,1064\,nm. This value is compatible with the theoretical prediction. Concerning Cotton-Mouton effect, our measurement is the second reported experimental value at this wavelength, and the first to agree at better than 1$\sigma$ with theoretical predictions.