The nonperturbative Gaussian effective potential is derived in the lam
bdaphi4-theory as the first nontrivial order of variational perturbati
on theory. In the framework of the proposed approach the algorithm of
calculating corrections is determined from the very beginning. Various
ways of constructing the variational procedure for the action functio
nal and questions about the convergence of the variational perturbatio
n theory series are discussed. The series convergence for the anharmon
ic variational perturbation theory functional is proved.