We investigate the properties of a sample of 35 galaxies, detected with the Atacama Large Millimeter/Submillimeter Array (ALMA) at 1.1 mm in the GOODS-ALMA field (area of 69 arcmin², resolution = 0.60″, rms ≃ 0.18 mJy beam⁻¹). Using the ultraviolet-to-radio deep multiwavelength coverage of the GOODS–South field, we fit the spectral energy distributions of these galaxies to derive their key physical properties. The galaxies detected by ALMA are among the most massive at z = 2−4 (M_{⋆, med} = 8.5 × 10¹⁰ M_⊙) and they are either starburst or located in the upper part of the galaxy star-forming main sequence. A significant portion of our galaxy population (∼40%), located at z ∼ 2.5 − 3, exhibits abnormally low gas fractions. The sizes of these galaxies, measured with ALMA, are compatible with the trend between the rest-frame 5000 Å size and stellar mass observed for z ∼ 2 elliptical galaxies, suggesting that they are building compact bulges. We show that there is a strong link between star formation surface density (at 1.1 mm) and gas depletion time: The more compact a galaxy’s star-forming region is, the shorter its lifetime will be (without gas replenishment). The identified compact sources associated with relatively short depletion timescales (∼100 Myr) are the ideal candidates to be the progenitors of compact elliptical galaxies at z ∼ 2.