We are developing a fully depleted silicon-on-insulator (FD-SOI) CMOS readout integrated circuit (ROIC) operated at temperatures below 4 K. Its application is planned for the readout circuit of high-impedance far-infrared detectors for astronomical observations. We designed a trans-impedance amplifier (TIA) using a CMOS operational amplifier (OPAMP) with FD-SOI technique. The TIA is optimized to readout signals from a germanium blocked impurity band (Ge BIB) detector which is highly sensitive to wavelengths of up to 200 m. For the first time, we demonstrated the FD-SOI CMOS OPAMP combined with the Ge BIB detector at 4.5 K. The result promises to solve issues faced by conventional cryogenic ROICs.