We take advantage of the exceptional photometric coverage provided by the combination of GALEX data in the UV and the ALHAMBRA survey in the optical and near-IR to analyze the physical properties of a sample of 1225 GALEX-selected Lyman break galaxies ( LBGs ) at 0.8 \lesssim z \lesssim 1.2 located in the COSMOS field . This is the largest sample of LBGs studied at that redshift range so far . According to a spectral energy distribution ( SED ) fitting with synthetic stellar population templates , we find that LBGs at z \sim 1 are mostly young galaxies with a median age of 341 Myr and have intermediate dust attenuation , \langle E _ { s } ( B - V ) \rangle \sim 0.20 . Due to their selection criterion , LBGs at z \sim 1 are UV-bright galaxies and have high dust-corrected total SFR , with a median value of 16.9 M _ { \odot } { yr } ^ { -1 } . Their median stellar mass is \log { \left ( M _ { * } / M _ { \odot } \right ) } = 9.74 . We obtain that the dust-corrected total SFR of LBGs increases with stellar mass and the specific SFR is lower for more massive galaxies ( downsizing scenario ) . Only 2 % of the galaxies selected through the Lyman break criterion have an AGN nature . LBGs at z \sim 1 are mostly located over the blue cloud of the color-magnitude diagram of galaxies at their redshift , with only the oldest and/or the dustiest deviating towards the green valley and red sequence . Morphologically , 69 % of LBGs are disk-like galaxies , with the fraction of interacting , compact , or irregular systems being much lower , below 12 % . LBGs have a median effective radius of 2.5 kpc and bigger galaxies have higher total SFR and stellar mass . Comparing to their high-redshift analogues , we find evidence that LBGs at lower redshifts are bigger , redder in the UV continuum , and have a major presence of older stellar populations in their SEDs . However , we do not find significant difference in the distributions of stellar mass or dust attenuation .