Ellipsometry is a powerful method for determining both the optical constants and thickness of thin films. For decades, solutions to ill-posed inverse ellipsometric problems require substantial human-expert intervention and have become essentially human-in-the-loop trial-and-error processes that are not only tedious and time-consuming but also limit the applicability of ellipsometry. Here, we demonstrate a machine learning based approach for solving ellipsometric problems in an unambiguous and fully automatic manner while showing superior performance. The proposed approach is experimentally validated by using a broad range of films covering categories of metals, semiconductors, and dielectrics. This method is compatible with existing ellipsometers and paves the way for realizing the automatic, rapid, high-throughput optical characterization of films.