In this article we prove that there exists an explicit bijection between nice d -pre-Calabi–Yau algebras and d -double Poisson differential graded algebras, where d \in \mathbb{Z} , extending a result proved by N. Iyudu and M. Kontsevich. We also show that this correspondence is functorial in a quite satisfactory way, giving rise to a (partial) functor from the category of d -double Poisson dg algebras to the partial category of d -pre-Calabi–Yau algebras. Finally, we further generalize it to include double P_{\infty} -algebras, introduced by T. Schedler.