The architectural differences between ASICs and FPGAs limit the effective performance gains achievable by the application of ASICbased approximation principles for FPGA-based reconfigurable computing systems. This paper presents a novel approximate multiplier architecture customized towards the FPGA-based fabrics, an efficient design methodology, and an open-source library. Our designs provide higher area, latency and energy gains along with better output accuracy than those offered by the state-of-the-art ASIC-based approximate multipliers. Moreover, compared to the multiplier IP offered by the Xilinx Vivado, our proposed design achieves up to 30%, 53%, and 67% gains in terms of area, latency, and energy, respectively, while incurring an insignificant accuracy loss (on average, below 1% average relative error). Our library of approximate multipliers is open-source and available online at https://cfaed.tudresden. de/pd-downloads to fuel further research and development in this area, and thereby enabling a new research direction for the FPGA community.