The ability to generate samples of the random effects from their conditional distributions is fundamental for inference in mixed effects models. Random walk Metropolis is widely used to perform such sampling, but this method is known to converge slowly for high dimensional problems, or when the joint structure of the distributions to sample is spatially heterogeneous. We propose an independent Metropolis-Hastings (MH) algorithm based on a multidimensional Gaussian proposal that takes into account the joint conditional distribution of the random effects and does not require any tuning. Indeed, this distribution is automatically obtained thanks to a Laplace approximation of the incomplete data model. We show that such approximation is equivalent to linearizing the structural model in the case of continuous data. Numerical experiments based on simulated and real data illustrate the performance of the proposed methods. In particular, we show that the suggested MH algorithm can be efficiently combined with a stochastic approximation version of the EM algorithm for maximum likelihood estimation in nonlinear mixed effects models.