Tensegrity structures provide durability and stability with minimal weight. Thanks to these properties, use of tensegrity structures for space applications is becoming an active research area. One of the main challenges is the automated construction of these structures. In this work, we present a framework for the automated assembly planning of tensegrity structures using an industrial robot equipped with a purpose-specific end-effector. We leverage the recent advances in sampling-based motion planning to create the motion strategies. Specifically, we divided the assembly planning problem into three stages. In the first stage, the initial position and orientation of the given tensegrity structure with respect to the assembly robot is determined using a motion-planning integrated forward elimination search. In the second stage, a feasible assembly sequence of the strings is found using backward disassembly search. Lastly, the individual robot motion plans for attaching each string to the bars for the given tensegrity configuration is generated using RRT∗. The efficacy of the framework was demonstrated using an extensive set of simulation experiments dealing with the assembly of a three-strut and nine-string tensegrity prism structure, which can be utilized as a building block of complex tensegrities.