The author establish global Morrey regularity and continuity results for weak solutions to asymptotically regular elliptic problems in divergence form \[ \begin{cases} \text{div}\, ({\mathbf a}(x,u,Du)+{\mathbf h}(x,u))= f(x,u,Du)& \text{ in } \Omega,\\ u=0 & \text{ on } \partial \Omega, \end{cases} \] where \(\Omega\subset \mathbb R^n\), \(n\geq 2\) is a bounded Reifenberg flat domain. The principal part of the operator is assumed to be merely asymptotically regular with respect to the gradient of a solution, which means that it behaves like the \(p\)-Laplacian operator for large values, while the lower order terms satisfy controlled growth conditions with respect to \(u\) and \(Du\), and the regularity in \(x\) is controlled by functions from Morrey spaces.