Which greek philosopher believed that, through purification, discipline, and successive rounds of births and deaths, the soul eventually merges with the divine?

The answer is Pythagoras. Though he was more notable in mathematics, Pythagoras contributed to Philosophy and psychology by connecting the physical properties to psychological harmony thus creating order in the physical world. Pythagoras is also known for his belief that the soul is immortal and there is a great possibility of reincarnation.