The LHCb experiment will be upgraded during LHC Long Shutdown 2 to be able to record data at a higher instantaneous luminosity. The readout rate is currently limited to 1 MHz by the Level 1 trigger. In order to achieve the target integrated luminosity of 50 fb−1 during LHC Run 3, all subdetectors have to be read out by a 40 MHz trigger-less readout system. Especially, the current tracking detectors downstream of the LHCb dipole magnet suffer from large detector dead times and a small granularity in the Outer Tracker, which consists of proportional straw tubes. Therefore, the Downstream Tracker will be replaced by a Scintillating Fibre Tracker with Silicon Photomultiplier readout. The total sensitive area of 340 m2 is made up of 2.5 m long fibre mats consisting of six staggered layers of 250 μm thin scintillating fibres. The scintillation light created by the charged particles traversing the fibre mats is transported to the fibre ends via total internal reflection and detected by state-of-the-art multi-channel SiPM arrays. This paper presents the detector concept, design, challenges, custom-made readout chips, as well as laboratory and beam test results.