The integral Bernstein center is an algebra that acts naturally on all smooth ell-adic representations of GL_n(F), for F a p-adic field. If one inverts ell this algebra has a nice description due to Bernstein and Deligne, but in the integral context it is much more complicated. We show that this algebra has a clean description in terms of the maximal tori of GL_n/F, and use this description to relate the Bernstein center to the deformation theory of Galois representations via local Langlands.