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A variational method for studying the ground state of strongly interacting quantum many-body bosonic systems is presented. Our approach constructs a class of extensive variational non-Gaussian wavefunctions which extend Gaussian states by means of nonlinear canonical transformations (NLCT) on the fields of the theory under consideration. We illustrate this method with the one dimensional Bose-Hubbard model for which the proposal presented here, provides a family of approximate ground states at arbitrarily large values of the interaction strength. We find that, for different values of the interaction, the non-Gaussian NLCT-trial states sensibly improve the ground state energy estimation when the system is in the Mott phase.