A theoretical study of the quasistationary process of stable growth of anisotropic dendrite under the conditions of convective heat and mass transfer in the melt was carried out. Based on the theory of morphological stability and the theory of microscopic solvability, a selection criterion is derived for the growth rate of the dendrite tip and its diameter in the case of convective heat and mass transfer, which determines the stable growth of a dendritic crystal with n-fold symmetry. A comparative analysis of the obtained selection criterion with the theoretical model under conductive boundary conditions and experimental data on the kinetics of dendrite growth in the Ti45Al55 alloy is performed.