We present a characterization of the physical properties of a sample of 35 securely-detected , dusty galaxies in the deep ALMA 1.2-mm image obtained as part of the ALMA Spectroscopic Survey in the Hubble Ultra Deep Field ( ASPECS ) Large Program . This sample is complemented by 26 additional sources identified via an optical/infrared source positional prior . Using their well-characterized spectral energy distributions , we derive median stellar masses and star formation rates ( SFR ) of 4.8 \times 10 ^ { 10 } ~ { } M _ { \sun } and 30 M _ { \sun } yr ^ { -1 } , and interquartile ranges of ( 2.4 - 11.7 ) \times 10 ^ { 10 } ~ { } M _ { \sun } and 20 - 50 ~ { } M _ { \sun } yr ^ { -1 } , respectively . We derive a median spectroscopic redshift of 1.8 with an interquartile range 1.1 - 2.6 , significantly lower than sub-millimeter galaxies detected in shallower , wide-field surveys . We find that 59 % \pm 13 % , 6 % \pm 4 % , and 34 % \pm 9 % of our sources are within , above and below \pm 0.4 dex from the SFR- stellar mass relation or main-sequence ( MS ) , respectively . The ASPECS galaxies closely follow the SFR-molecular gas mass relation and other previously established scaling relations , confirming a factor of five increase of the gas-to-stellar mass ratio from z = 0.5 to z = 2.5 , and a mild evolution of the gas depletion timescales with a typical value of 0.7 Gyr at z = 1 - 3 . ASPECS galaxies located significantly below the MS , a poorly exploited parameter space , have low gas-to-stellar mass ratios of \sim 0.1 - 0.2 and long depletion timescales > 1 Gyr . Galaxies along the MS dominate the cosmic density of molecular gas at all redshifts . Systems above the main sequence have an increasing contribution to the total gas reservoirs from z < 1 to z = 2.5 , while the opposite is found for galaxies below the MS .