Born in 1545 in the parish of Penmachno, near Betws-y-Coed, in Wales, Morgan was educated at Gwydir Grammar School in Wales, and then at St John's College, Cambridge where he studied a range of subjects including philosophy, mathematics and Greek. He received a BA in 1568 and an MA in 1571 before spending seven years on 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 with a BD in 1578 and a DD in 1583.
In addition to his scholarly pursuits, William Morgan was an ordained minister, having been ordained in 1568 by the Bishop of Ely. His first (part-time) appointment was to the parish of Llanbadarn Fawr, in 1572; he later moved to Welshpool (near the English border) in 1575 and then to Llanrhaedr-ym-Mochnant in 1578, which he took as a full-time duty.
Morgan was at university 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 as well. He began work on a 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.