In this paper, for the first time, a dynamic tunable graphene-based cross Yagi–Uda antenna in the terahertz region has been investigated comprehensively by two numerical methods and analytical analysis. To verify the accuracy of the analytical solution based on the coupled dipole method to obtain the directivity pattern, two numerical methods of finite-element and finite-difference time-domain have been used. Numerical results are well matched with the theoretical ones. By introducing the tunable cross Yagi–Uda antenna with graphene-coated spheres, different directivity radiation patterns such as omni-, vertical and horizontal bi- and quad-directional have been obtained with the maximum directivities of 2.42, 12.4, 12.3, and 10.5 dBi, respectively. Moreover, the effect of different element shapes including cube and cylinder on the directivity and radiation efficiency has been studied. Also, the new idea of multiple-access and controlling the user’s access to the radiated optical electromagnetic waves from the transmitting antenna has been studied as an optical wireless on-chip link. Finally, the effect of structural parameters on the directivity of the proposed antenna has been surveyed with the tolerance of ±5% to investigate the imperfections that may appear in the fabrication process.