In this paper, we study composition operators on the Hilbert space of complex-valued harmonic functions in the unit disc, focusing on their boundedness and structural properties. We analyze how analytic self-maps of the disc determine the behavior of the induced operators and extend several classical results from spaces of analytic functions to Hilbert space of complex-valued harmonic setting. We identify classes of analytic self-maps that generate isometric composition operators and prove that the boundedness of a composition operator implies that its symbol is a self-map of the disc. Boundedness is further characterized using Poisson integral estimates and integral mean techniques, which yield norm inequalities capturing the interaction between the analytic and co-analytic components of complex-valued harmonic functions. These inequalities provide refined upper and lower bounds for the operator norm in terms of the symbol evaluated at the origin, highlighting differences between harmonic and purely analytic theories. Additionally, we examine the relationship between reproducing kernels and composition operators, demonstrating that the adjoints of composition operators map reproducing kernels into reproducing kernels. This property leads to a characterization of composition operators via their adjoints and clarifies the structure of bounded operators on this space. Together, these results establish a comprehensive framework for understanding bounded composition operators in the context of Hilbert space of complex-valued harmonic functions.