We study the variability of solar activity using new photospheric proxies originally developed for the analysis of stellar magnetism with the CoRoT and Kepler photometric observations. These proxies were obtained by tracking the temporal modulations in the observations associated with the spots and magnetic features as the Sun rotates. We analyzed 21 yr of observations, spanning solar cycles 23 and 24, collected by the space-based photometric VIRGO and radial velocity GOLF instruments on board the SoHO satellite. We then calculated the photospheric activity proxy Sph is for each of the three VIRGO photometers and the associated Svel proxy from the radial velocity GOLF observations. Comparisons with several standard solar activity proxies sensitive to different layers of the Sun demonstrate that these new activity proxies, Sph and Svel, provide a new manner to monitor solar activity. We show that both the long- and short-term magnetic variabilities respectively associated with the 11-yr cycle and the quasi-biennial oscillation are well monitored, and that the magnetic field interaction between the subsurface, photosphere, and chromosphere of the Sun was modified between Cycle 24 and Cycle 23. Furthermore, the photometric proxies show a wavelength dependence of the response function of the solar photosphere among the three channels of the VIRGO photometers, providing inputs for the study of the stellar magnetism of Sun-like stars.