We construct <i>U</i>(2) noncommutative multi-instanton solutions by extending Witten's ansatz which reduces the problem of cylindrical symmetry in four dimensions to that of a set of Bogomol'nyi equations for an Abelian Higgs model in two-dimensional curved space. Using the Fock space approach, we give explicit vortex solutions to the Bogomol'nyi equations and, from them, we present multi-instanton solutions.Facultad de Ciencias Exactas