Once Zayn al-’Abidin (‘a) came to know of Yazid's consent, he asked him for the heads so that he would bury them. Yazid showed no hesitation to do so, ordering the heads, including those of Zayn al-’Abidin's family members, to be handed over to him. Zayn al-’Abidin reunited them with their respective bodies.
Writers of biographies who recorded his bringing the heads to Karbala’ include the author of Shaikh ‘Abbas al-Qummi, Nafs al-Mahmum who discusses this issue on p. 253 of his book, and it is also discussed on p. 155 of Riyad al-Ahzan of al-Qazwini.
As regarding al-Husayn's head, we read about it on p. 165 of al-Fattal's book Rawdat al-Wa’izin, and on p. 85 of Muthir al-Ahzan by Ibn Nama al-Hilli. The latter reference is the one the Shi’as consider as the most accurate as stated on p. 112 of Al-Luhuf by Ibn Tawus.
On p. 151 of al-Tabarsi's book I’lam al-Wara, as well as on p. 154 of Maqtal al-’Awalim, as is the case with both Riyad al-Maa'ib and Bihar al-Anwar, the same view is the most famous among scholars. On p. 200, Vol. 2, of his book titled Al-Manaqib, Ibn Shahr Ashub says, “In some of his letters, al-Murtada has stated that al-Husayn's head was reunited with its body in Karbala’.”
Al-Tusi has said that that incident was the basis for ziyarat al-Arba’yin. The author of Bihar al-Anwar cites Al-’Udad al-Qawiyya by the brother of ‘Allama al-Hilli. On p. 67 of his book ‘Aja'ib al-Makhluqat, al-Qazwini indicates that it was on the twentieth of Safar that al-Husayn's head was returned to its body.
Al-Shabrawi says, “The head was returned to the body after forty days.”1 According to Ibn Hajar's book Sharh al-Busiri's Hamziyya2, forty days after his martyrdom, al-Husayn's head was returned [to its body]. Sibt Ibn al-Jawzi has said, “It is most widely known that it [the head] was returned to Karbala’ and buried with the body.”3
On p. 57, Vol. 1, of his book Al-Kawakib al-Durriyya, al-Manawi records the consensus among Imamite Shi’as that the head was returned to Karbala’, and that this view was the one accepted by al-Qurtubi. He did not list his sources but attributed it to “some people of knowledge as well as eye witnesses,” becoming evident to him that the head was, indeed, returned to Karbala’. Abul-Rayhan al-Biruni states that it was on the twentieth of Safar that al-Husayn's head was reunited and buried with its body.4
Based on the above, any statements to the contrary should not be taken seriously especially those claiming that he was buried with his father (‘a), a claim with which the scholars mentioned above are familiar and which they all discard. Their rejection of such a claim proves that it cannot be relied upon especially since its isnad is not complete and its narrators are not famous. Abu Bakr al-'Alusi, who was asked once where the head of al-Husayn (‘a) was, composed the following verses:
Seek not al-Husayn's head in the east or in the west,
Leave all and come to me: in my heart does it rest.

References
1. al-Shabrawi, Al-Ithaf bi hHubbil-Ashraf, p. 12.
2. “Hamziyya” means a poem the rhyme of which ends with a hamza. N. Tr.
3. Ibn al-Jawzi, the grandson, Tathkirat al-Khawass p. 150.
4. Abul-Rayhan al-Biruni, Al-Athar al-Baqiya, Vol. 1, p. 331.