Background: Quantifying gene expression by RNA-Seq has several advantages over microarrays, including greater dynamic range and gene expression estimates on an absolute, rather than a relative scale. Nevertheless, microarrays remain in widespread use, demonstrated by the ever-growing numbers of samples deposited in public repositories.Results: We propose a novel approach to microarray analysis that attains many of the advantages of RNA-Seq. This method, called Machine Learning of Transcript Expression (MaLTE), leverages samples for which both microarray and RNA-Seq data are available, using a Random Forest to learn the relationship between the fluorescence intensity of sets of microarray probes and RNA-Seq transcript expression estimates. We trained MaLTE on data from the Genotype-Tissue Expression (GTEx) project, consisting of Affymetrix gene arrays and RNA-Seq from over 700 samples across a broad range of human tissues.Conclusion: This approach can be used to accurately estimate absolute expression levels from microarray data, at both gene and transcript level, which has not previously been possible. This methodology will facilitate re-analysis of archived microarray data and broaden the utility of the vast quantities of data still being generated.