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Linear mixed models (LMMs) can be applied in the meta-analyses of responses from individuals across multiple contexts, increasing power to detect associations while accounting for confounding effects arising from within-individual variation. However, traditional approaches to fitting these models can be computationally intractable. Here, we describe an efficient and exact method for fitting a multiple-context linear mixed model. Whereas existing exact methods may be cubic in their time complexity with respect to the number of individuals, our approach for multiple-context LMMs (mcLMM) is linear. These improvements allow for large-scale analyses requiring computing time and memory magnitudes of order less than existing methods. As examples, we apply our approach to identify expression quantitative trait loci from large-scale gene expression data measured across multiple tissues as well as joint analyses of multiple phenotypes in genome-wide association studies at biobank scale.