Mammalian gene expression patterns, and their variability across populations of cells, are regulated by factors specific to each gene in concert with its surrounding cellular and genomic environment. Lentiviruses such as HIV integrate their genomes into semi-random genomic locations in the cells they infect, and the resulting viral gene expression provides a natural system to dissect the contributions of genomic environment to transcriptional regulation. Previously, we showed that expression heterogeneity and its modulation by specific host factors at HIV integration sites are key determinants of infected-cell fate and a possible source of latent infections. Here, we assess the integration context dependence of expression heterogeneity from diverse single integrations of a HIV-promoter/GFP-reporter cassette in Jurkat T-cells. Systematically fitting a stochastic model of gene expression to our data reveals an underlying transcriptional dynamic, by which multiple transcripts are produced during short, infrequent bursts, that quantitatively accounts for the wide, highly skewed protein expression distributions observed in each of our clonal cell populations. Interestingly, we find that the size of transcriptional bursts is the primary systematic covariate over integration sites, varying from a few to tens of transcripts across integration sites, and correlating well with mean expression. In contrast, burst frequencies are scattered about a typical value of several per cell-division time and demonstrate little correlation with the clonal means. This pattern of modulation generates consistently noisy distributions over the sampled integration positions, with large expression variability relative to the mean maintained even for the most productive integrations, and could contribute to specifying heterogeneous, integration-site-dependent viral production patterns in HIV-infected cells. Genomic environment thus emerges as a significant control parameter for gene expression variation that may contribute to structuring mammalian genomes, as well as be exploited for survival by integrating viruses.