What is the Islamic explanation of the transmigration of souls?

The transmigration of souls (reincarnation) is the transfer of the soul after the death of the body to inhabit another body. This is among the most false of falsehoods and the greatest disbelief (kufr) because it is a denial of the Day of Reckoning, Paradise, and Hellfire. The Qur’an and Sunnah (definition) are replete with verses and hadiths that affirm resurrection and accountability, such as the Almighty’s saying: (Every soul shall taste death; then to Us you will be returned), and His ﷺ saying: "Indeed, you will be gathered barefoot, unclothed, and uncircumcised." Furthermore, the torment and blessings of the grave confirm that the soul does not transmigrate; rather, it is tormented or blessed along with the body. The people of Islam have unanimously agreed on deeming those who affirm transmigration as disbelievers, due to its indulgence in desires and denial of resurrection. It is obligatory to advise anyone holding this belief and call them to repentance; otherwise, it is obligatory to warn against them.