Context. Blazars are among the most energetic objects in the Universe. In 2008 August, Fermi/LAT detected the blazar PKS 1502+106 showing a rapid and strong gamma-ray outburst followed by high and variable flux over the next months. This activity at high energies triggered an intensive multi-wavelength campaign covering also the radio, optical, UV, and X-ray bands indicating that the flare was accompanied by a simultaneous outburst at optical/UV/X-rays and a delayed outburst at radio bands. Aims: In the current work we explore the phenomenology and physical conditions within the ultra-relativistic jet of the gamma-ray blazar PKS 1502+106. Additionally, we address the question of the spatial localization of the MeV/GeV-emitting region of the source. Methods: We utilize ultra-high angular resolution mm-VLBI observations at 43 and 86 GHz complemented by VLBI observations at 15 GHz. We also employ single-dish radio data from the F-GAMMA program at frequencies matching the VLBI monitoring. Results: PKS 1502+106 shows a compact core-jet morphology and fast superluminal motion with apparent speeds in the range 5--22 c. Estimation of Doppler factors along the jet yield values between ~7 up to ~50. This Doppler factor gradient implies an accelerating jet. The viewing angle towards the source differs between the inner and outer jet, with the former at ~3 degrees and the latter at ~1 degree, after the jet bends towards the observer beyond 1 mas. The de-projected opening angle of the ultra-fast, magnetically-dominated jet is found to be (3.8 +/- 0.5) degrees. A single jet component can be associated with the pronounced flare both at high-energies and in radio bands. Finally, the gamma-ray emission region is localized at less than 5.9 pc away from the jet base.