Converts fumarylacetoacetate to acetoacetate and fumarate. Involved in tyrosine catabolic pathway. Catalyzes the final step in the tyrosine degradation pathway. 4-fumarylacetoacetate + H2O = acetoacetate + fumarate + H(+) Amino-acid degradation; L-phenylalanine degradation; acetoacetate and fumarate from L-phenylalanine: step 6/6. Belongs to the FAH family.