Abstract: We introduce the class of split regular biHom-Poisson algebras as the natural generalization of split regular Hom-Poisson algebras. By developing techniques of connections of roots for this kind of algebras, we show that such a split regular biHom-Poisson algebras B is of the form B = U + \sum\nolimits_\alpha I_\alpha with U a subspace of a maximal abelian subalgebra H and any I_\alpha , a well described ideal of B, satisfying I_\alpha ,I_\beta + I_\alpha I_\beta = 0 if \alpha \ne \beta . Under certain conditions, in the case of B being of maximal length, the simplicity of the algebra is characterized.