Metabolomics research often requires the use of multiple analytical platforms, batches of samples, and laboratories, any of which can introduce a component of unwanted variation. In addition, every experiment is subject to within-platform and other experimental variation, which often includes unwanted biological variation. Such variation must be removed in order to focus on the biological information of interest. We present a broadly applicable method for the removal of unwanted variation arising from various sources for the identification of differentially abundant metabolites and, hence, for the systematic integration of data on the same quantities from different sources. We illustrate the versatility and the performance of the approach in four applications, and we show that it has several advantages over the existing normalization methods.