We discuss the formation of bound states made of two interacting atoms moving in a one dimensional (1D) quasi-periodic optical lattice. The underlying hamiltonian is the Aubry-André model with additional on-site interactions. We derive the quantum phase diagram for localization of both attractively and repulsively bound pairs. We calculate the pair binding energy and show analytically that its behavior as a function of the interaction strength depends crucially on the nature -extended, multifractal, localized- of the single-particle atomic states. Experimental implications of our results are discussed. Ref: G. Dufour, G. Orso, Phys. Rev. Lett. 109, 155306 (2012)