We present the Australian Square Kilometre Array Pathfinder localization and follow-up observations of the host galaxy of the repeating fast radio burst (FRB) source, FRB 20201124A, the fifth such extragalactic repeating FRB with an identified host. From spectroscopic observations using the 6.5 m MMT Observatory, we derive a redshift z = 0.0979 ± 0.0001, a star formation rate inferred from Hα emission SFR(Hα) ≈ 2.1 M⊙ yr-1, and a gas-phase metallicity of 12+log(O/H) ≈ 9.0. By jointly modeling the 12 filter optical-mid-infrared (MIR) photometry and spectroscopy of the host, we infer a median stellar mass of ∼2 × 1010 M⊙, internal dust extinction AV ≈ 1-1.5 mag, and a mass-weighted stellar population age of ∼5-6 Gyr. Connecting these data to the radio and X-ray observations, we cannot reconcile the broadband behavior with strong active galactic nucleus activity and instead attribute the dominant source of persistent radio emission to star formation, likely originating from the circumnuclear region of the host. The modeling also indicates a hot dust component contributing to the MIR luminosity at a level of ∼10%-30%. We model the host galaxy's star formation and mass assembly histories, finding that the host assembled >90% of its mass by 1 Gyr ago and exhibited a fairly constant SFR for most of its existence, with no clear evidence of past starburst activity.