  We prove a derived version of the Gabriel-Popescu theorem in the framework of
dg-categories and t-structures. This exhibits any pretriangulated dg-category
with a suitable t-structure (such that its heart is a Grothendieck abelian
category) as a t-exact localization of a derived dg-category of dg-modules. We
give an original proof based on a generalization of Mitchell's argument in "A
quick proof of the Gabriel-Popesco theorem" and involving derived injective
objects. As an application, we also give a short proof that derived categories
of Grothendieck abelian categories have a unique dg-enhancement.
