Most signals detected by genome-wide association studies map to non-coding sequence and their tissue-specific effects influence transcriptional regulation. However, key tissues and cell-types required for functional inference are absent from large-scale resources. Here we explore the relationship between genetic variants influencing predisposition to type 2 diabetes (T2D) and related glycemic traits, and human pancreatic islet transcription using data from 420 donors. We find: (a) 7741 cis-eQTLs in islets with a replication rate across 44 GTEx tissues between 40% and 73%; (b) marked overlap between islet cis-eQTL signals and active regulatory sequences in islets, with reduced eQTL effect size observed in the stretch enhancers most strongly implicated in GWAS signal location; (c) enrichment of islet cis-eQTL signals with T2D risk variants identified in genome-wide association studies; and (d) colocalization between 47 islet cis-eQTLs and variants influencing T2D or glycemic traits, including DGKB and TCF7L2. Our findings illustrate the advantages of performing functional and regulatory studies in disease relevant tissues.