We present Star Formation Histories ( SFHs ) for a sample of 104 massive ( stellar mass M > 10 ^ { 10 } M _ { \odot } ) quiescent galaxies ( MQGs ) at z = 1.0–1.5 from the analysis of spectro-photometric data from the SHARDS and HST/WFC3 G102 and G141 surveys of the GOODS-N 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 ( sSFR=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 % ) by galaxies with young mass-weighted ages , \overline { t _ { M } } < 2 Gyr , short star formation timescales , \langle \tau \rangle \sim 60-200 Myr , and masses log ( M/M _ { \odot } ) \sim 10.5 . There is an older population ( 15 % ) with \overline { t _ { M } } = 2 – 4 Gyr , longer star formation timescales , \langle \tau \rangle \sim 400 Myr , and larger masses , log ( M/M _ { \odot } ) \sim 10.7 . The SFHs of our MQGs are consistent with the slope and the location of the Main Sequence ( MS ) of star-forming galaxies at z > 1.0 , when our galaxies were 0.5-1.0 Gyr old . According to these SFHs , all the MQGs experienced a Luminous Infrared Galaxy ( LIRG ) phase that lasts for \sim 500 Myr , and half of them an Ultra Luminous Infrared Galaxy ( ULIRG ) phase for \sim 100 Myr . We find that the MQG population is almost assembled at z \sim 1 , and continues evolving passively with few additions to the population .