Diamond burnishing (DB) is a low-cost and reliable finishing process that dramatically improves the performance of metal components due to the favorable combination of surface integrity characteristics: a mirror-like surface, high surface microhardness, residual compressive stresses, and a grain-refined structure of the surface and nearby subsurface layers. This article aims to establish the effects of DB on surface height (Ra) and shape (Rsk and Rku) roughness parameters of 304 austenitic stainless steel specimens. DB was implemented on a CNC lathe using a spherical-ended polycrystalline diamond insert with a radius of 2 mm and flood lubrication. The steel, with a hardness of 250 HB, was tested in its as-received state. A planned experiment with a second-order composition plan, analysis of variance, and regression analyses were used to achieve the goal. The significance of the process governing factors was established via an analysis of the dimensionless absolute values of the first-order coefficients in the regression models. Explicit correlations between the main governing factors (burnishing force, feed rate, and burnishing velocity) of the DB process and the selected roughness parameters were found. The results obtained allow for the optimal selection of the DB governing factor magnitudes depending on the functional purpose of the processed component.