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The complex structure of inhomogeneous welds poses a long-standing challenge in ultrasonic non-destructive testing. Elongated grains with spatially varying dominant orientations can distort and split the ultrasonic beam, hindering inspection data interpretation. One way to tackle this problem is to include material information in imaging and signal analysis; however, such information is often only gathered using destructive methods. This paper reports the development of a physics-based weld inversion strategy determining grain orientations using a ray tomography principle. The considered approach does not rely on a macroscopic weld description but may incorporate it to facilitate inversion. Hence, it is more general than other available approaches. The methodology is demonstrated in both numerical and experimental examples. The experimental work focuses on mock-up samples from the nuclear industry and a sample manufactured during this research. The 'ground truth' for the latter comes from an EBSD evaluation—the most accurate (yet destructive) examination technique available. Across the considered specimens, our methodology yielded orientation maps with average errors well below 20∘ , leading to time-of-flight errors below 0.05 μs. Applying the result from inversion to ultrasonic imaging offered between 5 and 14 dB signal-to-noise ratio improvement for defect signatures. [ABSTRACT FROM AUTHOR]