Digital holograms fully encode the wavefield of light, thereby having many applications both for 3D object measurements as well as for display purposes, accounting for all human visual cues. Because the statistics and properties of holographic signals differ considerably from natural imagery such as photographs, conventional coding solutions will be sub-optimal. In this paper, we propose the integer Fresnel transform, which is - to our knowledge - the first lossless transform tailored for hologram coding. By combining the proposed transform with JPEG 2000, we report bit-rate savings from 0.12 up to 2.83 bits per channel on a collection of 8 digital holograms obtained from 3 different databases.