The proximity of the Large and Small Magellanic Clouds (LMC and SMC) provides the opportunity to study the impact of dwarf–dwarf interactions on their mass assembly with a unique level of detail. To this end, we analyze two-filter broadband imaging of 83 Hubble Space Telescope (HST) pointings covering 0.203 deg2 toward the SMC, extending out to ∼3.5 kpc in projection from its optical center. Lifetime star formation histories (SFHs) fit to each pointing independently reveal an outside-in age gradient such that fields in the SMC outskirts are older on average. We measure radial gradients of the look-back time to form 90%, 75%, and 50% of the cumulative stellar mass for the first time, finding δ(τ
90, τ
75, τ
50)/δ
R = (0.61
−
0.07
+
0.08
,
0.65
−
0.08
+
0.09
,
0.82
−
0.16
+
0.12
) Gyr kpc−1 assuming PARSEC evolutionary models and a commonly used elliptical geometry of the SMC, although our results are robust to these assumptions. The wing of the SMC deviates from this trend, forming 25% of its cumulative mass over the most recent 3 Gyr owing to a best-fit star formation rate that remains approximately constant. Our results are consistent with chemodynamical evidence of a tidally stripped SMC component in the foreground and imply contributions to the observed SFH from multiple previous LMC–SMC interactions. We also compare our SMC SFH with results from a companion study of the LMC, finding that while the two galaxies present different internal, spatially resolved SFH trends, both the LMC and SMC have similar near-constant lifetime SFHs when viewed globally.