We establish necessary and sufficient conditions for a sequence of d-dimensional vectors of multiple stochastic integrals F_d^k = (F₁^k, ..., F_d^k)\mathbf{F}_{d}^{k} = (F_{1}^{k}, \dots, F_{d}^{k}) , k ³ 1k\geq 1 , to converge in distribution to a d-dimensional Gaussian vector N_d = (N₁, ..., N_d)\mathbf{N}_{d} = (N_{1}, \dots, N_{d}) . In particular, we show that if the covariance structure of F_d^k converges to that of N_d, then componentwise convergence implies joint convergence. These results extend to the multidimensional case the main theorem of [10].