Non-planar field effect transistor (FET) devices having wrap-around source/drain contacts are provided, as well as methods for fabricating non-planar FET devices with wrap-around source/drain contacts. A method includes forming a non-planar FET device on a substrate, which includes a semiconductor channel layer, and a gate structure in contact with upper and sidewall surfaces of the semiconductor channel layer. First and second source/drain regions are formed on opposite sides of the gate structure in contact with the semiconductor channel layer. First and second recesses are formed in an isolation layer below bottom surfaces of the first and second source/drain regions, respectively. A layer of metallic material is deposited to fill the first and second recesses in the isolation layer with metallic material and form first and second source/drain contacts which surround the first and second source/drain regions.