One of the most important problems in classical mechanics is how to transform from Newtonian to Lagrangian description. We propose to put this problem in the context of the Poisson bracket. Apart from suggesting a simple method for finding a transformation to a variational approach by systematic determination of a Lagrangian from Newton's equations of motion, the main result of this work is the demonstration of a new connection that the Poisson bracket expressed in terms of generalized coordinates and velocities has with the Helmholtz conditions. We comment also on the nonuniqueness of the Lagrangian.