The Mu3e experiment searches for charged lepton flavor violation in the rare decay μ→eee with a projected sensitivity of 10−16. A precise measurement of the decay product momenta, decay vertex and time is necessary for background suppression at rates of 109 muons/s. This can be achieved by combining an ultra-lightweight pixel tracker based on HV-MAPS with two timing systems. The trigger-less readout of the detector with three stages of FPGA-boards over multi GBit/s optical links into a GPU filter farm is presented. In this scheme data from all sub-detectors is merged and distributed in time slices to the filter farm.