Leukocyte telomere length (LTL) is a heritable trait with two potential sources of heritability (h2): inherited variation in non-telomeric regions (e.g., SNPs that influence telomere maintenance) and variability in the lengths of telomeres in gametes that produce offspring zygotes (i.e., "direct" inheritance). Prior studies of LTL h2 have not attempted to disentangle these two sources. Here, we use a novel approach for detecting the direct inheritance of telomeres by studying the association between identity-by-descent (IBD) sharing at chromosome ends and phenotypic similarity in LTL. We measured genome-wide SNPs and LTL for a sample of 5069 Bangladeshi adults with substantial relatedness. For each of the 6318 relative pairs identified, we used SNPs near the telomeres to estimate the number of chromosome ends shared IBD, a proxy for the number of telomeres shared IBD (Tshared). We then estimated the association between Tshared and the squared pairwise difference in LTL ((ΔLTL)2) within various classes of relatives (siblings, avuncular, cousins, and distant), adjusting for overall genetic relatedness (ϕ). The association between Tshared and (ΔLTL)2 was inverse among all relative pair types. In a meta-analysis including all relative pairs (ϕ > 0.05), the association between Tshared and (ΔLTL)2 (P = 0.01) was stronger than the association between ϕ and (ΔLTL)2 (P = 0.43). Our results provide strong evidence that telomere length (TL) in parental germ cells impacts TL in offspring cells and contributes to LTL h2 despite telomere "reprogramming" during embryonic development. Applying our method to larger studies will enable robust estimation of LTL h2 attributable to direct transmission of telomeres.