The practice is based on the hadith of the Prophet, peace and blessings be upon him, and this is the opinion of al-Thawri and al-Shafi'i.

Chapter 59 (1)
909 - Ali ibn Khashram narrated to us, saying: Isa ibn Yunus narrated to us, from Ibn Jurayj, from Abu al-Zubayr, from Jabir, who said: The Prophet, peace and blessings be upon him, would stone the Jamrah on the Day of Sacrifice in the forenoon, and after that, after the sun had passed its zenith (2).
This is a good and authentic hadith.
The practice according to most scholars is that one does not stone after the Day of Sacrifice except after the sun has passed its zenith.

Chapter 60: What has been reported concerning departing from Muzdalifah before sunrise
910 - Qutaybah narrated to us, saying: Abu Khalid al-Ahmar narrated to us, from al-A'mash, from al-Hakam, from Miqsam--------------------------------------------
(1) The title of this chapter in the printed edition is: "Chapter on what has been reported concerning stoning on the Day of Sacrifice in the forenoon."
(2) Authentic; narrated by Muslim (1299) (314), Abu Dawud (1971), Ibn Majah (3053), al-Nasa'i 5/270, and it is in al-Musnad (14354), and Sahih Ibn Hibban (3886).
His saying "duhan" with tanwin, meaning: the time of the forenoon from after sunrise until before the sun's zenith.