A chromatic dispersion compensation apparatus for automatic compensation of chromatic dispersion of signals transmitted via an optical link at predetermined wavelengths of WDM channels within a predetermined band. A tapping unit taps optical signals received by the chromatic dispersion compensation apparatus via the optical link at predetermined wavelengths and supply them to an optical coherent receiver adapted to tune its local oscillator to WDM channels to generate corresponding analog electrical signals of the WDM channels which are sampled by an analog digital converter to provide digital signal samples of WDM channels processed by a digital signal processor of the chromatic dispersion compensation apparatus to calculate an estimate residual chromatic dispersion value of the received optical signals. A tuneable dispersion compensation module is set to perform optical compensation of a residual chromatic dispersion of the received optical signals depending on calculated estimate residual chromatic dispersion value of the received optical signals.