Morgan was born in 1545 at T? Mawr Wybrnant, in the parish of Penmachno, near Betws-y-Coed, North Wales. As his father was a tenant of the Gwydir estate, he was probably educated at Gwydir Castle, near Llanrwst, along with the children of the Wynn family. Morgan then attended St John's College, Cambridge where he studied a range of subjects including philosophy, mathematics and Greek. He graduated BA in 1568 and MA in 1571, before seven years of Biblical studies, including a study of the Bible in Greek, Hebrew and Aramaic and the works of the Church Fathers and contemporary Protestant theologians. He graduated BD in 1578 and DD in 1583.
In addition to his scholarly pursuits, Morgan was a clergyman of the Church of England, having been ordained in 1568 by the Bishop of Ely. His first clerical benefice was the parish of Llanbadarn Fawr, which he gained in 1572; in 1575 he moved to Welshpool, near the English border, and then to Llanrhaeadr-ym-Mochnant in 1578, which he took on as a full-time care of souls.
Morgan was still at Cambridge when William Salesbury published his Welsh New Testament in 1567. While he was pleased that this work was available, Morgan firmly believed in the importance of having the Old Testament translated into Welsh as well. He began work on his own translation of the Old Testament in the early 1580s and published this, together with a revision of Salesbury's New Testament, in 1588.
Following the publication of his Bible, Morgan worked on a revision of the Prayer Book (which had also been translated by Salesbury), published in 1599. He also began work on a revision of the 1588 Bible, which contained a number of printing errors. This work was continued after Morgan's death by Bishop Richard Parry and Dr John Davies, and a revised version of the Bible was published in 1620. This edition is still known as William Morgan's translation, and it is this rather than the previous edition which became the standard Welsh Bible until the 20th century and continues to be used to this day.
William Morgan was appointed Bishop of Llandaff in 1595 and moved to the bishopric of St Asaph in 1601. He died in 1604.
His achievement is now looked on as a major monument in the history of the Welsh language; it meant that the Welsh people could read the Bible in their first language at roughly the same time as their English neighbours had the privilege.