Inverse geodynamo modelling seeks to estimate the dynamic state of Earth's core from geo-magnetic data and the statistical information brought by a prior self-consistent, 3-D numerical model of the geodynamo. The method rests on the use of least-squares inversions under constraints and estimates hidden quantities by taking advantage of linear relations and long-range statistical correlations with the magnetic observations. The data, together with their error statistics, are provided by geomagnetic field models COV-OBS, gufm-sat-Q3 and CM4, covering epochs 1840–2010. The prior numerical model is the recently published coupled Earth dynamo, the output of which presents a high degree of morphological semblance to the geomagnetic field while reproducing the main features of its secular variation. An analysis of the inversion misfits to the data shows that the prior model generally accounts well for the main field and secular variation data within their specified errors, throughout the investigated time period. Inverted core flows are confirmed to be mainly organized in columns parallel to the Earth's rotation axis. A previously observed giant eccentric columnar gyre of westward-drifting flow is found to be present from epoch 1870 onwards, and its structure is shown to slowly rotate westwards at a rate up to 0.1 • yr −1 , confirming an earlier prediction based on direct numerical modelling. Temporal variations in the axisymmetric part of the gyre accurately account for observed variations of the length of the day in recent epochs. Inverted magnetic structures support a mechanism of azimuthal flux expulsion by convective columns to explain the origin of low-latitude magnetic flux patches existing beneath the Atlantic. The 1840–2010 time average of the inverted density anomaly field has a longitudinal hemispheric structure, with most of the buoyancy in the Eastern hemisphere, consistent with rapid surges of convective columns imaged in this hemisphere, with earlier proposals of a faster inner core freezing there, and with a possible east-to-west convective translation of the solid inner core. The typical timescales of flow variation observed in the inversions are two to three times shorter than those naturally produced by a direct simulation of the prior model, underlining its limits in fully rendering the Earth's core short timescale dynamics.