When the DNA double helix is subjected to external forces it can stretch elastically to elongations reaching 100% of its natural length. These distortions, imposed at the mesoscopic or macroscopic scales, have a dramatic effect on electronic properties at the atomic scale and on electrical transport along DNA. Accordingly, a multiscale approach is necessary to capture the electronic behavior of the stretched DNA helix. To construct such a model, we begin with accurate density-functional-theory calculations for electronic states in DNA bases and base pairs in various relative configurations encountered in the equilibrium and stretched forms. These results are complemented by semi-empirical quantum mechanical calculations for the states of a small size [18 base pair poly(CG)-poly(CG)] dry, neutral DNA sequence, using previously published models for stretched DNA. The calculated electronic states are then used to parametrize an effective tight-binding model that can describe electron hopping in the presence of environmental effects, such as the presence of stray water molecules on the backbone or structural features of the substrate. These effects introduce disorder in the model hamiltonian which leads to electron localization. The localization length is smaller by several orders of magnitude in stretched DNA relative to that in the unstretched structure.