Given two n-variable Boolean functions f and g, we study the problem of computing an ε-approximate isomorphism between them. An ε-approximate isomorphism is a permutation π of the n Boolean variables such that and differ on at most an ε fraction of all Boolean inputs . We give a randomized time algorithm that computes an ε-approximate isomorphism between two isomorphic Boolean functions f and g that are given by depth d circuits of size, where d is a constant independent of n, for any positive ε. In contrast, the best known algorithm for computing an exact isomorphism between n-ary Boolean functions has running time [12] even for functions computed by size DNF formulas. Our algorithm is based on a result for hypergraph isomorphism with bounded edge size [4] and the classical Linial–Mansour–Nisan result on approximating small depth and size Boolean circuits by small degree polynomials using Fourier analysis [11].