  We fully characterize regular Hom-Lie structures on the incidence algebra
$I(X,K)$ of a finite connected poset $X$ over a field $K$. We prove that such a
structure is the sum of a central-valued linear map annihilating the Jacobson
radical of $I(X,K)$ with the composition of certain inner and multiplicative
automorphisms of $I(X,K)$.
