Multistep synthesis performed on solid support is a powerful means to generate small-molecule libraries for the discovery of chemical probes to dissect biological mechanisms as well as for drug discovery. Therefore, expansion of the collection of robust chemical transformations amenable to solid-phase synthesis is desirable for achieving chemically diverse libraries for biological testing. Here, we show that sulfur(VI) fluoride exchange (SuFEx) chemistry, exemplified by pairing phenols with aryl fluorosulfates, can be used for the solid-phase synthesis of biologically active compounds. As a case study, we designed and synthesized a library of 84 hydroxamic acid-containing small molecules, providing a rich source of inhibitors with diverse selectivity profiles across the human histone deacetylase enzyme family. Among other discoveries, we identified a scaffold that furnished inhibitors of HDAC11 with exquisite selectivity in vitro and a selective inhibitor of HDAC6 that was shown to affect the acetylation of α-tubulin over histone sites H3K18, H3K27, as well as SMC3 in cultured cells. Our results encourage the further use of SuFEx chemistry for the synthesis of diverse small-molecule libraries and provide insight for future design of selective HDAC inhibitors.