Detailed models of alpha Cen A and B based on new seismological data for alpha Cen B by Carrier & Bourban (2003) have been Computed using the Geneva evolution code including atomic diffusion. Taking into account the numerous observational constraints now available for the alpha Cen system, we find a stellar model which is in good agreement with the astrometric, photometric, spectroscopic and asteroseismic data. The global parameters of the alpha Cen system are now firmly constrained to an age of t=6.52+/-0.30 Gyr, an initial helium mass fraction Y-i=0.275+/-0.010 and an initial metallicity (Z/X)(i)=0.0434+/-0.0020. Thanks to these numerous observational constraints, we confirm that the mixing-length parameter alpha of the B component is larger than the one of the A component, as already suggested by many authors (Noels et al. 1991; Fernandes Neuforge 1995; Guenther & Demarque 2000): alpha(B) is about 8% larger than alpha(A) (alpha(A)=1.83+/-0.10 and alpha(B)=1.97+/-0.10). Moreover, we show that asteroseismic measurements enable to determine the radii of both stars with a very high precision (errors smaller than 0.3%). The radii deduced from seismological data are compatible with the new interferometric results of Kervella et al. (2003) even if they are slightly larger than the interferometric radii (differences smaller than 1%).