We present I-band Surface Brightness Fluctuations (SBF) measurements for 15 early type galaxies (3 giants, 12 dwarfs) in the central region of the Centaurus cluster, based on VLT FORS1 imaging data. From the SBF-distances to our sample galaxies we determine the distance of the Centaurus cluster to be 41.3 +/- 2.1 Mpc (33.08 +/- 0.11 mag), about the same distance as of the ``Great Attractor''. We find a distance difference of 0.27 +/- 0.34 mag between the two subcomponents Cen30 and Cen45, ruling out that both components are separated by their Hubble flow distance. A distance difference of 0.48 +/- 0.21 mag is found between the central galaxies NGC 4696 (Cen30) and NGC 4709 (Cen45) of both components, supported by the different turn-over magnitudes of their respective globular cluster systems. This suggests that Cen45 is falling into but has not yet reached Cen30, supporting the idea of a large scale filament along the line of sight towards Centaurus (Churazov et al. 1999). H_0=83.0 +/- 8.3 km/s/Mpc is obtained for our Cen30 sample. This value corresponds to a much smaller Hubble flow distortion in the direction of Centaurus than determined by Tonry et al. (2000), implying that the GA mass estimate by Tonry et al. may be too high and/or that the Centaurus cluster falls into the GA almost perpendicularly to the line of sight. As our mean single measurement error is very close to the measured distance scatter of the investigated galaxies, we can only derive an upper limit of +/- 10 Mpc radial extension for the Centaurus cluster. No evidence for an infall pattern into the Great Attractor is found within the uncertainties for the 11 galaxies with measured redshift.

16 pages, 10 figures, accepted for publication in A&A