Opacity-driven shifts of the apparent very long baseline interferometry (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 γ-ray blazar 3C 454.3 using direct measurements from simultaneous 4.6-43 GHz very long baseline array observations, and a time lag analysis of 4.8-37 GHz light curves from the University of Michigan Radio Observatory, Crimean Astrophysical Observatory and Metsähovi observations in 2007-2009. The results support the standard Königl model of jet physics in the VLBI core region. The distance of the core from the jet origin r c(ν), the core size W(ν) and the light curve time lag ΔT(ν) all depend on the observing frequency ν as r c(ν) ∝ W(ν) ∝ ΔT(ν) ∝ ν−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(ν) and W(ν) 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/1 pc)−0.8 G. The total kinetic power of electron/positron jet is about 1044 ergs s−1.