We report the discovery of TOI-677b, first identified as a candidate in light curves obtained within Sectors 9 and 10 of the Transiting Exoplanet Survey Satellite (TESS) mission and confirmed with radial velocities. TOI-677b has a mass of M_p_=1.236_-0.067_^+0.069^M_J_, a radius of R_P_=1.170{+/-}0.03R_J_, and orbits its bright host star (V=9.8mag) with an orbital period of 11.23660{+/-}0.00011d, on an eccentric orbit with e=0.435{+/-}0.024. The host star has a mass of M_=1.181{+/-}0.058M{sun}, a radius of R=1.28-0.03_^+0.03^R_{sun}, an age of 2.92-0.73_^+0.80^Gyr and solar metallicity, properties consistent with a main-sequence late-F star with T_eff_=6295{+/-}77K. We find evidence in the radial velocity measurements of a secondary long-term signal, which could be due to an outer companion. The TOI-677b system is a well-suited target for Rossiter-Mclaughlin observations that can constrain migration mechanisms of close-in giant planets.