We perform a complete analysis of isospin breaking in K --> 2pi amplitudes in chiral perturbation theory, including both strong isospin violation (m(u) not equal m(d)) and electromagnetic corrections to next-to-leading order in the low-energy expansion. The unknown chiral couplings are estimated at leading order in the 1/N-c expansion. We study the impact of isospin breaking on CP conserving amplitudes and rescattering phases. In particular, we extract the effective couplings g8 and g27 from a fit to K --> pipi branching ratios, finding small deviations from the isospin-limit case. The ratio Re A(0)/ Re A(2) measuring the DeltaI = 1/2 enhancement is found to decrease from 22.2 +/- 0.1 in the isospin limit to 20.3 +/- 0.5 in the presence of isospin breaking. We also analyze the effect of isospin violation on the CP violation parameter epsilon', finding a destructive interference between three different sources of isospin violation. Within the uncertainties of large-N-c estimates for the low-energy constants, the isospin violating correction for epsilon' is below 15%.