Near-infrared bandpasses on spaceborne observatories diverge from their ground-based counterparts as they are free of atmospheric telluric absorption. Available transformations between respective filter systems in the literature rely on theoretical stellar atmospheres, which are known to have difficulties reproducing the observed spectral energy distributions of cool giants. We present new transformations between the Two Micron All Sky Survey JHKS and Hubble Space Telescope WFC3/IR F110W, F125W, and F160W photometric systems based on synthetic photometry of empirical stellar spectra from four spectral libraries. This sample comprises over 1000 individual stars, which together span nearly the full H-R diagram and sample stellar populations from the solar neighborhood out to the Magellanic Clouds, covering a broad range of ages, metallicities, and other relevant stellar properties. In addition to global color-dependent transformations, we examine band-to-band differences for cool, luminous giant stars in particular, including multiple types of primary distance indicators.