A solution of the target-rapidity Balitsky-Kovchegov (BK) equation is presented considering, for the first time, the complete impact-parameter dependence, i.e. including the orientation of the dipole with respect to the impact-parameter vector. To address the non-local behaviour introduced in the target-rapidity formulation of the BK equation, three different prescriptions are considered to take into account the rapidities preceding the initial condition value. The solutions are used to compute the structure functions of the proton and the diffractive photo- and electro-production of J/𝜓. These predictions agree well with HERA data, confirming that the target-rapidity Balitsky-Kovchegov equation with the full impact-parameter dependence is a viable tool to study the small Bjorken-𝑥 limit of perturbative QCD at current facilities like RHIC and LHC as well as in future colliders like the EIC, for which we present predictions for DIS and diffractive vector meson production.