We experimentally observe common-signal-induced synchronization between two semiconductor lasers driven by a broadband optical noise signal. We use a super-luminescent diode as a source of the optical noise signal, whose bandwidth is over THz. Synchronization is achieved even without injection locking between the drive noise signal and the semiconductor lasers, however, the optical wavelengths of the two semiconductor lasers need to be precisely matched. We investigate the parameter dependence of synchronization on the injection strength of the drive signal and the relaxation oscillation frequency of the semiconductor lasers. We apply optical band-pass-filters to change the bandwidth of the noise signal, and investigate the quality of synchronization. We found that high-quality synchronization can be achieved when the bandwidth of the optical spectra of the semiconductor lasers are within the bandwidth of the optical noise signal.