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Recent studies have revealed the counterintuitive possibility that increasing disorder can turn a topologically trivial insulator into a nontrivial insulator, called a topological Anderson insulator (TAI). Here, we propose and experimentally demonstrate a photonic TAI in a two-dimensional disordered gyromagnetic photonic crystal in the microwave regime. We directly observe the disorder-induced topological phase transition from a trivial insulator to a TAI with robust chiral edge states. We also demonstrate topological heterostructures that host edge states at interfaces between domains with different disorder parameters.