High Schottky barrier heights at metal–semiconductor junctions due to Fermi-level pinning can degrade the performance of electronic devices and increase their energy consumption. Van der Waals contacts between metals and two-dimensional semiconductors without Fermi-level pinning are theoretically possible, but have not been achieved due to the presence of interactions such as interface defects and orbital overlap. Here we show that interaction- and defect-free van der Waals contacts can be formed between a range of metals and two-dimensional semiconductors via a metal deposition process that uses a selenium buffer layer. Our contacts obey the Schottky–Mott rule and have a Fermi-level pinning of –0.91. A comparison between the van der Waals contacts and typical direct metal contacts reveals differences in interface gap distances, band bending and electrical characteristics. Using gold van der Waals contacts, we fabricate p-type tungsten diselenide field-effect transistors that exhibit stable operation with on/off ratio of 106, mobility of 155 cm2 (V s)–1, contact resistance of 1.25 kΩ μm and Schottky barrier height of 60 meV.