We show that the new precise measurements of Cosmic Microwave Background
(CMB) temperature and polarization anisotropies made by the Planck satellite
significantly improves previous constraints on the cosmic gravitational waves
background (CGWB) at frequencies $f>10^{-15}$ Hz. On scales smaller than the
comoving horizon at the time of decoupling, primordial gravitational waves
contribute to the total radiation content of the Universe. Considering
adiabatic perturbations, CGWB affects temperature and polarization CMB power
spectra and matter power spectrum in a manner identical to relativistic
particles. Considering the latest Planck results we constrain the CGWB energy
density to $\Omega_{\rm gw} h^2 <2.5\times 10^{-6} $ at 95\% c.l. Combining CMB
power spectra with lensing, BAO and primordial Deuterium abundance
observations, we obtain $\Omega_{\rm gw} h^2 <1.7\times 10^{-6} $ at 95\% c.l.,
improving previous cosmological bounds by a factor 5 and the recent direct
upper limit from the LIGO and VIRGO experiments by 50\%. A combined analysis of
future satellite missions as CORE and EUCLID could improve current bound by a
factor $\sim20$.