We establish the maximal regularity for nonautonomous Ornstein–Uhlenbeck operators in L p -spaces with respect to a family of invariant measures, where $${p \in (1, +\infty)}$$ . This result follows from the maximal L p -regularity for a class of elliptic operators with unbounded, time-dependent drift coefficients and potentials acting on $${L^{p}(\mathbb{R}^{N} )}$$ with Lebesgue measure.