The Milky Way’s Nuclear Star Cluster (NSC) provides a unique opportunity to resolve the stellar population and study star formation in this extreme environment. Earlier studies that assumed uniform solar metallicity in NSC stars may have biased age estimates due to the age-metallicity degeneracy in star formation histories. We report the first star formation history of the Milky Way’s NSC that includes extensive stellar metallicity measurements from Gemini and VLT within the central 1.5 pc. Photometry and spectroscopy of 770 late-type stars are forward modeled with a Bayesian inference, finding the best fit with a two-component model. The dominant component contains 93% +/- 3% of the mass, is metal-rich ([M/H] ~ 0.45), and has an age of 5 +3/-2 Gyr, which is ∼3 Gyr younger than earlier studies with fixed (solar) metallicity; this younger age challenges coevolutionary models in which the NSC and supermassive black holes formed simultaneously at early times. The minor population component has low metallicity ([M/H] ~ -1.1) and contains ∼7% of the stellar mass. The age of the minor component is uncertain (0.1–5 Gyr old). We also provide refined predictions on compact remnant numbers and their gravitational-wave merger rates. These predictions result in 2–4 times fewer neutron stars compared to earlier predictions that assume solar metallicity, introducing a possible new path to understand the so-called “missing-pulsar problem”.