We show how to formulate celestial twistor amplitudes in Yang-Mills (YM) and gravity. This is motivated by a refined holographic correspondence between the twistor transform and the light transform in the boundary Lorentzian CFT. The resulting amplitudes are then equivalent to light transformed correlators on the celestial torus. Using an ambidextrous basis of twistor and dual twistor variables, we derive formulae for the three and four-point YM and gravity amplitudes. The four-point amplitudes take a particularly simple form in terms of elementary functions, with a striking correspondence between the YM and gravity expressions. We derive celestial twistor BCFW recursion relations and show how these may be used to generate the four-point YM amplitude, illuminating the structure it inherits from the three-point amplitude and paving the way for the calculation of higher multiplicity light transformed correlators. Throughout our calculations we utilise the unique properties of the boundary structure of split signature, and in order to properly motivate and highlight these properties we first develop our methodology in Lorentzian signature. This also allows us to prove a holographic correspondence between Fourier transforms in Lorentzian signature and shadow transforms in the Euclidean boundary CFT.

56 pages plus appendices, v2:minor typos fixed, v3:minor correction, v4:edited for submission