TransitFit fits exoplanetary transit light-curves for transmission spectroscopy studies. The code uses nested sampling for efficient and robust multi-epoch, multi-wavelength fitting of transit data obtained from one or more telescopes. TransitFit allows per-telescope detrending to be performed simultaneously with parameter fitting, including the use of user-supplied detrending alogorithms. Host limb darkening can be fitted either independently ("uncoupled") for each filter or combined ("coupled") using prior conditioning from the PHOENIX stellar atmosphere models. For this, TransitFit uses the Limb Darkening Toolkit (ascl:1510.003) together with filter profiles, including user-supplied filter profiles.