The present paper extends the asymptotic matching techniques developed by Brumberg and Kopejkin as Applied to the relativistic theory of astronomical reference systems, in the following principal aspects. (1) The full post-Newtonian expressions for the gravitational field in the geocentric reference system are given in closed form. This cancels the necessity to use a post-Newtonian analogue of the ''tidal'' expansion in powers of local spatial coordinates to represent the gravitational field of the external masses (such as the Sun). A finite expression, analogous to the classical third-body perturbation function, can be used instead. (2) Our approach, being initially developed in harmonic coordinates, can be easily reformulated in other most frequently used gauges. The corresponding transformation formulas in the case of the standard parametrized-post-Newtonian gauge are derived. (3) In applying our theory to astronomical problems, the equations of motion of an Earth satellite are derived with the use of the geodetic principle. We do not neglect herewith relativistic terms proportional to the nongeodesic acceleration of the Earth. A practically important improvement of some previous results is obtained. The results of this paper are thoroughly compared with those derived by Brumberg and Kopejkin in terms of multiple expansions.