Hazrat Mahdi (as) is descended from the line of the Prophet (saas)

Narrated by Ali (ra), the Messenger of Allah (saas) said:

Even if there remains only one day for the world, Allah, the Exalted, will send a man from the Ahl al-Bayt (People of the House). (Sunan Abu Dawud, 5:92)

Days and nights will not end until one [Hazrat Mahdi (as)] from my Ahl al-Bayt rules the entire world. (Al-Uqayli, An-Najmu's-saqib fi Bayan Anna'l Mahdi min Awladi Ali b. Abu Talib Ale't-Tamam wa al-Qamal)

Hazrat Mahdi (as) is from the line of my daughter Fatima. (Sunan Ibn Majah, 10:348)

Hear the glad tidings of Hazrat Mahdi (as). He is one from the Quraysh and from my Ahl al-Bayt. (Al-Muttaqi al-Hindi, Al-Burhan fi Alamat al-Mahdi Akhir az-Zaman, p. 13)

Hazrat Mahdi (as) is one of my children. His face is like a star shining in the sky. (Ali Ibn Sultan Muhammad al-Qaari al-Harawi al-Hanafi, Risalat Mashrab al Vardi fi Mazhabi 'l Mahdi)

All prophets are related to one another. Hazrat Mahdi (as) will also be of that line. These descendants are popularly known as sayyid. Hazrat Mahdi (as) will also be sayyid.

Allah refers in the Qur’an to messengers all related to one another. These verses indicate that Hazrat Mahdi (as) will share that same line of descent.

Allah chose Adam and Noah and the family of Abraham and the family of 'Imran over all other beings – descendants one of the other. Allah is All-Hearing, All-Knowing. (Surah Al 'Imran, 33-34)

“Our Lord, make us both Muslims submitted to You, and our descendants a Muslim community submitted to You. Show us our rites of worship and turn towards us. You are the Ever-Returning, the Most Merciful.” (Surat al-Baqara, 128)

And some of their forebears, descendants and brothers; We chose them and guided them to a straight path. (Surat al-An'am, 87)