The existence of smooth hyperboloidal initial data sets for the vacuum Einstein equations with non-zero cosmological constant is studied. Supposing that the trace of the (physical) second fundamental form of the initial hypersurface is constant, there is a correspondence between the solutions of the vacuum constraints with and without cosmological constant, respectively. This enables us to extend the results proved by Andersson and Chrusciel about the smoothness of the initial data with zero cosmological constant to the case .