Algebraically Compact Categories
I found the reference for CPO-like categories.
Scott's paper Continuous Lattices in the book Toposes, Algebraic Geometry and Logic. It is explained in the comments right after corollary 4.3.
A more general theorem can be found in Smyth's and Plotkin's paper Category-Theoretic Solution of Recursive Domain Equations. It is lemma 2.

However, again, the functors are not arbitrary. One needs some sort of a continuity assumption.