Reverse osmosis (RO) has shown itself to be a viable technology for the treatment and minimization of industrial and domestic wastewater streams. The current research presents a deterministic branch-and-bound global optimization-based algorithm for the solution of the reverse osmosis network (RON) synthesis problem. The mathematical programming model describes the RON through nonconvex mixed-integer nonlinear programs(MINLPs). A piecewise mixed-integer linear program (MILP) is derived based on the convex relaxation of the nonconvex terms present in the MINLP formulation to approximate the original nonconvex program and to obtain a valid lower bound on the global optimum. The MILP model is solved at every node in the branch-and-bound tree to verify the global optimality of the treatment network within a pre-specified gap tolerance. Several constraints are developed to simultaneously screen the treatment network alternatives during the search, tighten the variable bounds, and consequently accelerate algorithm convergence. Water desalination is considered as a case study to illustrate the global optimization of the RO network.