  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
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 <1.7\times 10^{-6} $ at 95\% CL. Combining CMB power
spectra with lensing, BAO and primordial Deuterium abundance observations, we
obtain $\Omega_{\rm gw} h^2 <1.2\times 10^{-6} $ at 95\% CL, improving previous
Planck bounds by a factor 3 and the recent direct upper limit from the LIGO and
VIRGO experiments a factor 2. A combined analysis of future satellite missions
as COrE and EUCLID could improve current bound by more than an order of
magnitude.
