Opacity-driven shifts of the apparent VLBI core position with frequency (the core shift effect) probe physical conditions in the innermost parts of jets in active galactic nuclei. We present the first detailed investigation of this effect in the brightest gamma-ray blazar 3C454.3 using direct measurements from simultaneous 4.6-43 GHz VLBA observations, and a time lag analysis of 4.8-37 GHz lightcurves from the UMRAO, CrAO, and Metsahovi observations in 2007-2009. The results support the standard Konigl model of jet physics in the VLBI core region. The distance of the core from the jet origin r_c(nu), the core size W(nu), and the lightcurve time lag DT(nu) all depend on the observing frequency nu as r_c(nu)~W(nu)~ DT(nu)~nu^-1/k. The obtained range of k=0.6-0.8 is consistent with the synchrotron self-absorption being the dominating opacity mechanism in the jet. The similar frequency dependence of r_c(nu) and W(nu) suggests that the external pressure gradient does not dictate the jet geometry in the cm-band core region. Assuming equipartition, the magnetic field strength scales with distance r as B = 0.4(r/1pc)^-0.8 G. The total kinetic power of electron/positron jet is about 10^44 ergs/s.