We have developed a highly integrated, fast and compact readout electronics for Silicon Photomultiplier (SiPM) based Time of Flight Positron Emission Tomography (TOF-PET) scanners. The readout is based on the use of TOP-PET Application Specific Integrated Circuit (PETsys TOFPETl ASIC) with 64 channels, each with its amplifier, discriminator, Time to Digital Converter (TDC) and amplitude determination using Time Over Threshold (TOT). The ASIC has 25 ps r.m.s. intrinsic time resolution and fully digital output. The system is optimised for high rates, good timing, low power consumption and low cost. For validating the readout electronics, we have built a technical PET scanner, hereafter called "demonstrator", with 2'048 SiPM channels. The PET demonstrator has 16 compact Detector Modules (DM). Each DM has two ASICs reading 128 SiPM pixels in one-to-one coupling to 128 Lutetium Yttrium Orthosilicate (LYSO) crystals measuring 3.1x3.1x15 mm 3 each. The data acquisition system for the demonstrator has two Front End Boards type D (FEB/D), each collecting the data of 1'024 channels (8 DMs), and transmitting assembled data frames through a serial link (4.8Gbps), to a single Data Acquisition (DAQ) board plugged into the Peripheral Component Interconnect Express (PCIe) bus of the data acquisition PC. Results obtained with this PET demonstrator are presented.