Parameter estimation is a central issue in system modeling, the tipical setting is to start with a given set of measurements and extract the parameters of a model supposed to describe the system under scrutiny. The recent availability of large datasets coming from the complex system has made even more pressing the quest for efficient models, and the related parameter extraction techniques. We study Ising chains with arbitrary multispin finite-range couplings, providing an explicit solution of the associated inverse Ising problem, i.e. the problem of inferring the values of the coupling constants from the correlation functions. As an application, we reconstruct the couplings of chain Ising Hamiltonians having exponential or power-law two-spin plus three- or four-spin couplings. The generalization of the method to ladders and to Ising systems where a mean-field interaction is added to general finite-range couplings is also discussed.