Thin-walled square and circular hollow steel tubes are designed to support the permanent and construction loads of several upper composite floors before filling the concrete into the tubes to form concrete-filled double steel tubular (CFDST) columns. The influences of preloads acting on the steel tubes on the structural responses of slender square CFDST columns have not been investigated either experimentally or numerically. This paper presents a fiber-based computational model for the determination of the interaction behavior of local and global buckling in axially and eccentrically loaded CFDST thin-walled square slender columns including preload effects. The computational modeling method accounts for the influences of the deformations induced by preloads, local-global interaction buckling, geometric imperfections, second-order, and geometric and material nonlinearities. The accuracy of the computational algorithms developed is validated by comparing computations with test data on concrete-filled steel tubular (CFST) columns and finite element results of double-skin CFST (DCFST) columns with preload effects. The computer algorithms are employed to quantify the influences of preloads on the local-global interaction buckling responses of CFDST columns with various important parameters. Proposed is a design method for calculating the ultimate loads of concentrically loaded slender square CFDST columns considering preloads. The computational and design models developed are shown to be efficient modeling and design tools for square CFDST slender columns taking into account the construction method of high-rise composite buildings.