Rapid characterization of the earthquake source and of its effects is a growing field of interest. Until recently, it still took several hours to determine the first-order attributes of a great earthquake (e.g. M_w≥ 7.5), even in a well-instrumented region. The main limiting factors were data saturation, the interference of different phases and the time duration and spatial extent of the source rupture. To accelerate centroid moment tensor (CMT) determinations, we have developed a source inversion algorithm based on modelling of the W phase, a very long period phase (100–1000 s) arriving at the same time as the P wave. The purpose of this work is to finely tune and validate the algorithm for large-to-moderate-sized earthquakes using three components of W phase ground motion at teleseismic distances. To that end, the point source parameters of all M_w≥ 6.5 earthquakes that occurred between 1990 and 2010 (815 events) are determined using Federation of Digital Seismograph Networks, Global Seismographic Network broad-band stations and STS1 global virtual networks of the Incorporated Research Institutions for Seismology Data Management Center. For each event, a preliminary magnitude obtained from W phase amplitudes is used to estimate the initial moment rate function half duration and to define the corner frequencies of the passband filter that will be applied to the waveforms. Starting from these initial parameters, the seismic moment tensor is calculated using a preliminary location as a first approximation of the centroid. A full CMT inversion is then conducted for centroid timing and location determination. Comparisons with Harvard and Global CMT solutions highlight the robustness of W phase CMT solutions at teleseismic distances. The differences in M_w rarely exceed 0.2 and the source mechanisms are very similar to one another. Difficulties arise when a target earthquake is shortly (e.g. within 10 hr) preceded by another large earthquake, which disturbs the waveforms of the target event. To deal with such difficult situations, we remove the perturbation caused by earlier disturbing events by subtracting the corresponding synthetics from the data. The CMT parameters for the disturbed event can then be retrieved using the residual seismograms. We also explore the feasibility of obtaining source parameters of smaller earthquakes in the range 6.0 ≤M_w < 6.5. Results suggest that the W phase inversion can be implemented reliably for the majority of earthquakes of M_w= 6 or larger.