For a local system and a function on a smooth complex algebraic variety, we give a proof of a conjecture of M. Kontsevich on a formula for the vanishing cycles using the twisted de Rham complex of the formal microlocalization of the corresponding locally free sheaf with integrable connection having regular singularity at infinity. We also prove its local version as well as its generalization to the case of the de Rham complexes of regular holonomic D-modules where we have to use the tensor product with a certain sheaf of formal microlocal differential operators instead of the formal completion.