‘Alā-al-Din Tabrizi was born around 1523 CE in Tabriz. His father was a hāfez (honorific title given to someone who has memorized the Qur'an) named Shams-al-Din Mohammad, and there is mention of him having been a student of Shams-al-Din Mohammad Tabrizi. So, he may have studied calligraphy with his father.
His first dated writing was produced in 957 AH/1550 CE. From the year 1565 CE onward he was associated with the court of Shāh Tahmāsp Safavi. His last surviving writing is dated to 1008 AH/1599 CE. He was a master of Naskh, Thuluth, Mohaqqaq, Rihān, and Reqā‘ and created many plaques in Tabriz that unfortunately have not survived to this day. Some of his most notable students were ‘Ali-Rezā ‘Abbāsi and ‘Abd-al-Bāqi Tabrizi both of whom are counted amongst the masters of Thuluth calligraphy.
‘Alā-al-Din spent most of his life in Tabriz, living a number of years in Qazvin until dying around 1601 CE.