Ultrafast and sensitive (noise equivalent power <1 nWHz-1/2) light-detection in the Terahertz (THz) frequency range (0.1-10 THz) and at room-temperature is key for applications such as time-resolved THz spectroscopy of gases, complex molecules and cold samples, imaging, metrology, ultra-high-speed data communications, coherent control of quantum systems, quantum optics and for capturing snapshots of ultrafast dynamics, in materials and devices, at the nanoscale. Here, we report room-temperature THz nano-receivers exploiting antenna-coupled graphene field effect transistors integrated with lithographically-patterned high-bandwidth (~100 GHz) chips, operating with a combination of high speed (hundreds ps response time) and high sensitivity (noise equivalent power <120 pWHz-1/2) at 3.4 THz. Remarkably, this is achieved with various antenna and transistor architectures (single-gate, dual-gate), whose operation frequency can be extended over the whole 0.1-10 THz range, thus paving the way for the design of ultrafast graphene arrays in the far infrared, opening concrete perspective for targeting the aforementioned applications.