Aims . In the framework of the multi-wavelength and very long baseline interferometry (VLBI) monitoring program TANAMI (Tracking Active Nuclei with Austral Milliarcsecond Interferometry), we study the evolution of the parsec-scale radio emission in radio galaxies in the southern hemisphere and their relationship to the γ -ray properties of the sources. Our study investigates systematically, for the first time, the relationship between the two energy regimes in radio galaxies. In this first paper, we focus on Fermi -LAT-detected sources. Methods . The TANAMI program monitors a large sample of radio-loud AGN at 8.4GHz and 22.3GHz with the Australian long baseline array (LBA) and associated telescopes in Antarctica, Chile, New Zealand and South Africa. We performed a kinematic analysis for five γ -ray detected radio galaxies using multi-epoch 8.4GHz VLBI images, deriving limits on intrinsic jet parameters such as speed and viewing angle. We analyzed 103 months of Fermi -LAT data in order to study possible connections between the γ -ray properties and thepc-scale jets of Fermi -LAT-detected radio galaxies, both in terms of variability and average properties. We discuss the individual source results and draw preliminary conclusions on sample properties including published VLBI results from the MOJAVE (Monitoring Of Jets in Active galactic nuclei with VLBA Experiments) survey, with a total of fifteen sources. boosting. This seems to indicate that γ -ray emission in radio galaxies is not driven by orientation-dependent e ff ects, as in blazars, in accordance with the unified model of jetted AGN.