  A homotopy Gerstenhaber structure on a differential graded algebra is
essentially a family of operations defining a multiplication on its bar
construction. We prove that the normalized singular cochain algebra of a
Davis-Januszkiewicz space is formal as a homotopy Gerstenhaber algebra, for any
coefficient ring. This generalizes a recent result by the author about
classifying spaces of tori and also strengthens the well-known dga formality
result for Davis-Januszkiewicz spaces due to the author and Notbohm-Ray. As an
application, we determine the cohomology rings of free and based loop spaces of
Davis-Januszkiewicz spaces.
