Aims:To conduct an intensive study of the rich, X-ray luminous galaxy cluster Abell 773 at z = 0.22 containing a diffuse radio halo to determine its dynamical status. Methods: Our analysis is based on new spectroscopic data obtained at the TNG telescope for 107 galaxies, 37 spectra recovered from the CFHT archive and new photometric data obtained at the Isaac Newton Telescope. We use statistical tools to select 100 cluster members (out to 1.8 h^-1_70 from the cluster centre), to analyse the kinematics of cluster galaxies and to determine the cluster structure. Our analysis is also performed by using X-ray data stored in the Chandra archive. Results: The 2D distribution shows two significant peaks separated by 2´ in the EW direction with the main western one closely located at the position of the two dominant galaxies and the X-ray peak. The velocity distribution of cluster galaxies shows two peaks at v 65000 and 67500 km s-1, corresponding to the velocities of the two dominant galaxies. The low velocity structure has a high velocity dispersion - σv = 800-1100 km s-1 - and its galaxies are centred on the western 2D peak. The high velocity structure has intermediate velocity dispersion - σv˜ 500 km s-1 - and is characterized by a complex 2D structure with a component centred on the western 2D peak and a component centred on the eastern 2D peak, these components probably being two independent groups. We estimate a cluster mass within 1h^-1_70 of 6-11h^-1_70 M_&sun;. Our analysis of Chandra data shows the presence of two very close peaks in the core and the elongation of the X-ray emission in the NEE-SWW direction. Conclusions: Our results suggest we are looking at probably two groups in an advanced stage of merging with a main cluster and having an impact velocity Δ {{v}_rf} 2300 km s-1. In particular, the radio halo seems to be related to the merger of the eastern group. Figures 1 and 2 are only available in electronic form at http://www.aanda.org Table 1 is only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/467/37