A technique for establishing the total neutron rate of a highly-collimated monochromatic cold neutron beam was demonstrated using an alpha–gamma counter. The method involves only the counting of measured rates and is independent of neutron cross sections, decay chain branching ratios, and neutron beam energy. For the measurement, a target of $^{10}$B-enriched boron carbide totally absorbed the neutrons in a monochromatic beam, and the rate of absorbed neutrons was determined by counting 478 keV gamma rays from neutron capture on $^{10}$B with calibrated high-purity germanium detectors. A second measurement based on Bragg diffraction from a perfect silicon crystal was performed to determine the mean de Broglie wavelength of the beam to a precision of 0.024%. With these measurements, the detection efficiency of a neutron monitor based on neutron absorption on $^{6}$Li was determined to an overall uncertainty of 0.058%. We discuss the principle of the alpha–gamma method and present details of how the measurement was performed including the systematic effects. We also describe how this method may be used for applications in neutron dosimetry and metrology, fundamental neutron physics, and neutron cross section measurements.