The epicardium is a mesothelial tissue layer that envelops the heart. Cardiac injury activates dynamic gene expression programs in epicardial tissue, which in zebrafish enables subsequent regeneration through paracrine and vascularizing effects. To identify tissue regeneration enhancer elements (TREEs) that control injury-induced epicardial gene expression during heart regeneration, we profiled transcriptomes and chromatin accessibility in epicardial cells purified from regenerating zebrafish hearts. We identified hundreds of candidate TREEs, which are defined by increased chromatin accessibility of non-coding elements near genes with increased expression during regeneration. Several of these candidate TREEs were incorporated into stable transgenic lines, with five out of six elements directing injury-induced epicardial expression but not ontogenetic epicardial expression in larval hearts. Whereas two independent TREEs linked to the gene gnai3 showed similar functional features of gene regulation in transgenic lines, two independent ncam1a-linked TREEs directed distinct spatiotemporal domains of epicardial gene expression. Thus, multiple TREEs linked to a regeneration gene can possess either matching or complementary regulatory controls. Our study provides a new resource and principles for understanding the regulation of epicardial genetic programs during heart regeneration. This article has an associated 'The people behind the papers' interview.