Can we make virtual characters in a scene interact with their surrounding objects through simple instructions? Is it possible to synthesize such motion plausibly with a diverse set of objects and instructions? Inspired by these questions, we present the first framework to synthesize the full-body motion of virtual human characters performing specified actions with 3D objects placed within their reach. Our system takes as input textual instructions specifying the objects and the associated intentions of the virtual characters and outputs diverse sequences of full-body motions. This is in contrast to existing work, where full-body action synthesis methods generally do not consider object interactions, and human-object interaction methods focus mainly on synthesizing hand or finger movements for grasping objects. We accomplish our objective by designing an intent-driven full-body motion generator, which uses a pair of decoupled conditional variational autoencoders (CVAE) to learn the motion of the body parts in an autoregressive manner. We also optimize for the positions of the objects with six degrees of freedom (6DoF) such that they plausibly fit within the hands of the synthesized characters. We compare our proposed method with the existing methods of motion synthesis and establish a new and stronger state-of-the-art for the task of intent-driven motion synthesis. Through a user study, we further show that our synthesized full-body motions appear more realistic to the participants in more than 80% of scenarios compared to the current state-of-the-art methods, and are perceived to be as good as the ground truth on several occasions.