In this work we present for the first time, to the best of our knowledge, a passively synchronized thulium (Tm) and erbium (Er) doped fiber laser mode-locked by a common graphene saturable absorber (GSA). The laser consists of two ring resonators combined with a 90 cm long common fiber branch incorporating the saturable absorber (SA). Such laser generates optical solitons centered at 1558.5 nm and 1938 nm with pulse durations of 915 fs and 1.57 ps, respectively. Both laser loops were passively synchronized at repetition frequency of 20.5025 MHz by nonlinear interaction (cross phase modulation, XPM) in common fiber branch between generated pulses. The maximum cavity mismatch of the Er-laser in synchronization regime was 0.78 mm. The synchronization mechanism was also investigated. We demonstrate that the third order nonlinearities of graphene enhance the synchronization range. In our case the range was increased about 85%. The integrated RMS timing jitter between the synchronized pulses was 67 fs.