  We calculate gauge instanton corrections to a class of higher derivative
string effective couplings introduced in [1]. We work in Type I string theory
compactified on K3xT2 and realise gauge instantons in terms of D5-branes
wrapping the internal space. In the field theory limit we reproduce the
deformed ADHM action on a general {\Omega}-background from which one can
compute the non-perturbative gauge theory partition function using
localisation. This is a non-perturbative extension of [1] and provides further
evidence for our proposal of a string theory realisation of the
{\Omega}-background.
