The turnover of sex-determining loci has repeatedly occurred in a number of species, rather than having a diverged pair of sex chromosomes. We model the turnover process by considering a linked locus under sexually antagonistic selection. The entire process of a turnover may be divided into two phases, which are referred to as the stochastic and deterministic phases. The stochastic phase is when a new sex-determining allele just arises and is still rare and random genetic drift plays an important role. In the deterministic phase, the new allele further increases in frequency by positive selection. The theoretical results currently available are for the deterministic phase, which demonstrated that a turnover of a newly arisen sex-determining locus could benefit from selection at a linked locus under sexually antagonistic selection, by assuming that sexually antagonistic selection works in a form of balancing selection. In this work, we provide a comprehensive theoretical description of the entire process from the stochastic phase to the deterministic phase. In addition to balancing selection, we explore several other modes of selection on the linked locus. Our theory allows us make a quantitative argument on the rate of turnover and the effect of the mode of selection at the linked locus. We also performed simulations to explore the pattern of polymorphism around the new sex-determining locus. We find that the pattern of polymorphism is informative to infer how selection worked through the turnover process.