We extend the theory of weighted norm inequalities on variable Lebesgue spaces to the case of bilinear operators.We introduce a bilinear version of the variable A p(•) condition and show that it is necessary and sufficient for the bilinear maximal operator to satisfy a weighted norm inequality.Our work generalizes the linear results of the first author, Fiorenza, and Neugebauer [7] in the variable Lebesgue spaces and the bilinear results of Lerner et al. [22] in the classical Lebesgue spaces.As an application we prove weighted norm inequalities for bilinear singular integral operators in the variable Lebesgue spaces.