A credible method for establishing the fuel burnup in a research reactor is highly valued. We developed and implemented a novel experimental method of measuring 235U depletion in irradiated fuel assemblies, and describe it in this paper, as well as report the results and their comparison to burnup-coupled Monte-Carlo core simulations. The new experimental method relies on gamma spectroscopic measurements, which were performed on irradiated HEU MTR fuel used in IRR1 (Israel Research Reactor 1, Soreq NRC). Using the new method, 235U depletion was determined from the transparency increase of the fuel assemblies with increasing depletion to 155keV gamma's (emitted from an activated Rhenium source situated beneath the fuel assembly, and reaching, through an air collimator, a Germanium detector positioned on the other side of the fuel). In addition, the more common method of measuring long-lived fission products concentration in the fuel (e.g., 137Cs) was performed by analyzing the obtained spectroscopic measurements. The measured data allowed obtaining high accuracy results in 20 axial points for each fuel assembly, with depletion uncertainty of less than 5% for the measured five assemblies. For the burnup simulations, we developed a coupled MCNP-DRAGON code and simulated the burnup of IRR1 cores since 1980 until 2017, using 3D model of the cores. We compared the results of the fuel's 235U depletion and 137Cs activity in the computation and experiment and found a very good match, to within the measured uncertainty in the depletion for all the assemblies. Finally, we examined the often-used 137Cs-based depletion approximation and found it is accurate to within 3-12% (absolute depletion), compared to the new depletion measurement method presented herein.