We develop a general setting for N = 2 rigid supersymmetric field theories with gauged central charge in harmonic superspace. We consider those N = 2 multiplets which have a finite number of off-shell components and exist off shell owing to a non-trivial central charge. This class includes, in particular, the hypermultiplet with central charge and various versions of the vector-tensor multiplet. For such theories we present a manifestly supersymmetric universal action. Chern-Simons couplings to an external N = 2 super Yang-Mills multiplet are given, in harmonic superspace, for both the linear and non-linear vector-tensor multiplets with gauged central charge. We show how to deduce the linear version of the vector-tensor multiplet from six dimensions.