This article summarizes a workshop held on March, 2014, on the potential of the James Webb Space Telescope (JWST) to revolutionize our knowledge of the physical properties of exoplanets through transit observations. JWST's unique combination of high sensitivity and broad wavelength coverage will enable the accurate measurement of transits with high signal-to-noise. Most importantly, JWST spectroscopy will investigate planetary atmospheres to determine atomic and molecular compositions, to probe vertical and horizontal structure, and to follow dynamical evolution, i.e. exoplanet weather. JWST will sample a diverse population of planets of varying masses and densities in a wide variety of environments characterized by a range of host star masses and metallicities, orbital semi-major axes and eccentricities. A broad program of exoplanet science could use a substantial fraction of the overall JWST mission.