Experimental bounds on induced vacuum magnetic birefringence can be used to improve present photon-photon scattering limits in the electronvolt energy range. Measurements with the Polarizzazione del Vuoto con Laser apparatus [E. Zavattini et al., Phys. Rev. D 77, 032006 (2008)] at both $\ensuremath{\lambda}=1064$ and 532 nm lead to bounds on the parameter ${A}_{e}$, describing nonlinear effects in QED, of ${A}_{e}^{(1064)}<6.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}21}\text{ }\text{ }{\mathrm{T}}^{\ensuremath{-}2}@1064\text{ }\text{ }\mathrm{nm}$ and ${A}_{e}^{(532)}<6.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}21}\text{ }\text{ }{\mathrm{T}}^{\ensuremath{-}2}@532\text{ }\text{ }\mathrm{nm}$, respectively, at 95% confidence level, compared to the predicted value of ${A}_{e}=1.32\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}\text{ }\text{ }{\mathrm{T}}^{\ensuremath{-}2}$. The total photon-photon scattering cross section may also be expressed in terms of ${A}_{e}$, setting bounds for unpolarized light of ${\ensuremath{\sigma}}_{\ensuremath{\gamma}\ensuremath{\gamma}}^{(1064)}<4.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}62}\text{ }\text{ }{\mathrm{m}}^{2}$ and ${\ensuremath{\sigma}}_{\ensuremath{\gamma}\ensuremath{\gamma}}^{(532)}<2.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}60}\text{ }\text{ }{\mathrm{m}}^{2}$. Compared to the expected QED scattering cross section these results are a factor of $\ensuremath{\simeq}2\ifmmode\times\else\texttimes\fi{}{10}^{7}$ higher and represent an improvement of a factor about 500 on previous bounds based on ellipticity measurements and of a factor of about ${10}^{10}$ on bounds based on direct stimulated scattering measurements.