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We estimate the population of black holes with luminous stellar companions (BH-LCs) in the Milky Way (MW) observable by Gaia. We evolve a realistic distribution of BH-LC progenitors from zero-age to the current epoch taking into account relevant physics, including binary stellar evolution, BH-formation physics, and star formation rate, in order to estimate the BH-LC population in the MW today. We predict that Gaia will discover between 3800 and 12,000 BH-LCs by the end of its mission, depending on BH natal kick strength and observability constraints. We find that the overall yield, and distributions of eccentricities and masses of observed BH-LCs, can provide important constraints on the strength of BH natal kicks. Gaia-detected BH-LCs are expected to have very different orbital properties compared to those detectable via radio, X-ray, or gravitational-wave observations.