We introduce enriched ∞-operads as certain presheaves which generalize Barwick's complete Segal operads. The simple structure of the indexing categories allows us to define algebras between enriched ∞-operads. By comparing this presheaf model with an enriched version of Moerdijk-Cisinski's dendroidal Segal spaces, we then prove a rectification theorem which states that the homotopy theory of ∞-operads enriched in a nice symmetric monoidal model category is equivalent to that of strictly enriched operads. From this we can easily infer that all established models for ∞-operads are equivalent to simplicially enriched operads.