Abstract. In this paper, we first introduce the notion of an anti-pre-Poisson bialgebra, which is shown to be equivalent to both quadratic anti-pre-Poisson algebras and matched pairs of Poisson algebras. The study of coboundary anti-pre-Poisson bialgebras leads to the anti-prePoisson Yang-Baxter equation (APP-YBE). Skew-symmetric solutions of this equation give rise to coboundary anti-pre-Poisson bialgebras. Furthermore, we investigate how solutions without skew-symmetry can also induce such bialgebras, prompting the introduction of quasi-triangular and factorizable anti-pre-Poisson bialgebras. In particular, solutions of the APP-YBE whose symmetric parts are invariant induce quasi-triangular anti-pre-Poisson bialgebras. Such solutions are characterized by relative Rota-Baxter operators with weights. Finally, we establish a one-to-one correspondence between quadratic Rota-Baxter anti-pre-Poisson algebras and factorizable anti-pre-Poisson bialgebras.