We present star formation histories (SFHs) for a sample of 104 massive (stellar mass M>10^10^M_{sun}_) quiescent galaxies (MQGs) at z=1.0-1.5 from the analysis of spectrophotometric data from the Survey for High-z Absorption Red and Dead Sources (SHARDS) and HST/WFC3 G102 and G141 surveys of the GOODS-North field, jointly with broad-band observations from ultraviolet (UV) to far-infrared (far-IR). The sample is constructed on the basis of rest-frame UVJ colours and specific star formation rates (sSFRs=SFR/Mass). The spectral energy distributions (SEDs) of each galaxy are compared to models assuming a delayed exponentially declining SFH. A Monte Carlo algorithm characterizes the degeneracies, which we are able to break taking advantage of the SHARDS data resolution, by measuring indices such as MgUV and D4000. The population of MQGs shows a duality in their properties. The sample is dominated (85 per cent) by galaxies with young mass-weighted ages, <t_M_><2Gyr, short star formation time-scales, <{tau}>~60-200MYr, and masses log(M/M_{sun}_)~10.5. There is an older population (15 per cent) with <t_M_>=2-4Gyr, longer star formation time-scales, <{tau}>~400Myr, and larger masses, log(M/M_{sun}_)~10.7. The SFHs of our MQGs are consistent with the slope and the location of the main sequence of star-forming galaxies at z>1.0, when our galaxies were 0.5-1.0Gyr old. According to these SFHs, all the MQGs experienced a luminous infrared galaxy phase that lasts for ~500Myr, and half of them an ultraluminous infrared galaxy phase for ~100Myr. We find that the MQG population is almost assembled at z~1, and continues evolving passively with few additions to the population.