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In this paper, we establish the cohomology of relative Rota–Baxter operators on Lie-Yamaguti algebras via the Yamaguti cohomology. Then, we use this type of cohomology to characterize deformations of relative Rota–Baxter operators on Lie-Yamaguti algebras. We show that if two linear or formal deformations of a relative Rota–Baxter operator are equivalent, then their infinitesimals are in the same cohomology class in the first cohomology group. Moreover, an order <i>n</i> deformation of a relative Rota–Baxter operator can be extended to an order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></semantics></math></inline-formula> deformation if and only if the obstruction class in the second cohomology group is trivial.