Selecting informative features, such as accurate biomarkers for disease diagnosis, prognosis and response to treatment, is an essential task in the field of bioinformatics. Medical data often contain thousands of features and identifying potential biomarkers is challenging due to small number of samples in the data, method dependence and non-reproducibility. This paper proposes a novel ensemble feature selection method, named Filter and Wrapper Stacking Ensemble (FWSE), to identify reproducible biomarkers from high-dimensional omics data. In FWSE, filter feature selection methods are run on numerous subsets of the data to eliminate irrelevant features, and then wrapper feature selection methods are applied to rank the top features. The method was validated on four high-dimensional medical datasets related to mental illnesses and cancer. The results indicate that the features selected by FWSE are stable and statistically more significant than the ones obtained by existing methods while also demonstrating biological relevance. Furthermore, FWSE is a generic method, applicable to various high-dimensional datasets in the fields of machine intelligence and bioinformatics.