The Buddhist view of rebirth refutes the notion of an immortal soul, because it denies that there is anything unchanging in either the physical or mental aspects of phenomena.

The Buddha categorised the prevalent theories of body and soul of his time into two distinct miscomprehensions. The first category comprised those that denied that the body and soul were separate — at death we become extinct, with no after or future life. The other group were those that thought body and soul were totally separate. The body is perishable, but the soul is immortal and continues to survive from one birth to another.

The first group he called “nihilists” and the second group “eternalists.” Interestingly, it is a situation not dissimilar to the one we face today, with the humanist materialists, on the one hand, denying the existence of mind or consciousness and rejecting any notion of survival after individual death, and the religious traditions, on the other hand, positing a soul that survives death and continues to exist in one form or another.

The Buddhist position on rebirth, on the contrary, is based on the so-called middle view, which avoids these two extremes, namely, the denial of the continuation of consciousness or mind altogether, and the positing of an immutable psychic principle (atman or soul, or some other descriptor of a greater self). According to the Buddha, both body and mind are subject to continual change, and so even at death what is transferred from one life to the next is not an unchanging psychic principle, but different psychic elements all hanging together, samskaras — memories, various impressions, and so on, none of which is unchanging in itself.

-- Traleg Kyabgon Rinpoche