We present a unified theoretical picture which studies simultaneously the γγ→π+π−, π0π0, K+K−, K0K0, π0η reactions up to about s=1.4 GeV reproducing the experimental cross sections. The present work implements in an accurate way the final state interaction of the meson-meson system, which is shown to be essential in order to reproduce the data, particularly the L=0 channel. This latter channel is treated here following a recent theoretical work in which the meson-meson amplitudes are well reproduced and the f0, a0, σ resonances show up clearly as poles of the t matrix. The present work, as done in earlier ones, also incorporates elements of chiral symmetry and exchange of vector and axial resonances in the crossed channels, as well as a direct coupling to the f2(1270) and a2(1370) resonances. We also evaluate the decay width of the f0(980) and a0(980) resonances into the γγ channel.