A geodynamo simulation is presented where the Earth's core density, rotation rate, convective power and electrical conductivity are matched, while viscous losses are maintained minor in the force balance and power budget. Improving over earlier preliminary calculations, the simulation is integrated over near 1700 years in physical time, and realistically renders the time scale range between interannual hydromagnetic waves and secular convective motions. The solution has been obtained by gradually approaching these conditions along a path in model parameter space. A quasi-geostrophic, magneto-Archimedes-Coriolis (QG-MAC) force balance is confirmed, with the characteristic length scale of the system remaining near the planetary scale. Without the need for extrapolation, the morphology, variations and dynamics of the velocity, convective density anomaly and magnetic fields are in excellent quantitative agreement with geomagnetic and geodetic observations supplied over the past centuries by navigation, observatories and satellites. In particular, the simulation reveals the contribution of interdecadal magneto-Coriolis waves to geomagnetic variations in the vicinity of 60-yr periods. This direct validation of the convective geodynamo paradigm additionally offers a quantitative and first principle-based physical link between the observable signals and deep Earth geodynamic parameters. The model confirms that a convective power (or Ohmic dissipation) level near 3 TW is needed to account for the observed geomagnetic variations, and that the top of the core should be convectively neutral or unstable. Explaining the core-originated interannual to decadal variations of the length of day through electromagnetic core-mantle coupling requires a lower mantle conductance on the order of 10^9 S. It may also become possible to constrain the outer core electrical conductivity from the observed patterns of interannual magneto-Coriolis waves. Finally, the simulation can be considered a reliable source of prior information for solving geomagnetic inverse and prediction problems.