ABSTRACT The distribution of gas and metals in the circumgalactic medium (CGM) plays a critical role in how galaxies evolve. The MUSE-ALMA Haloes survey combines MUSE, ALMA, and HST observations to constrain the properties of the multiphase gas in the CGM and the galaxies associated with the gas probed in absorption. In this paper, we analyse the properties of galaxies associated with 32 strong ${\rm H\, {\small I}}$ Ly-α absorbers at redshift 0.2 ≲ z ≲ 1.4. We detect 79 galaxies within ±500 kms−1 of the absorbers in our 19 MUSE fields. These associated galaxies are found at physical distances from 5.7 kpc and reach star formation rates as low as 0.1 M⊙ yr−1. The significant number of associated galaxies allows us to map their physical distribution on the Δv and b plane. Building on previous studies, we examine the physical and nebular properties of these associated galaxies and find the following: (i) 27/32 absorbers have galaxy counterparts and more than 50 per cent of the absorbers have two or more associated galaxies, (ii) the ${\rm H\, {\small I}}$ column density of absorbers is anticorrelated with the impact parameter (scaled by virial radius) of the nearest galaxy as expected from simulations, (iii) the metallicity of associated galaxies is typically larger than the absorber metallicity, which decreases at larger impact parameters. It becomes clear that while strong ${\rm H\, {\small I}}$ absorbers are typically associated with more than a single galaxy, we can use them to statistically map the gas and metal distribution in the CGM.