[1] Born in Reykjavík, the son of bishop Sigurbjörn Einarsson and his wife, Magnea Þorkelsdóttur, he graduated from Reykjavík High School in 1957.
He returned to Iceland in 1962, and hosted a regular radio show on RÚV for many years.
He is best known for composing music (in 1973) for the 13th-century Icelandic hymn, Heyr, himna smiður.
In 1993, Þorkell was awarded the Knight's Cross of the Icelandic Order of the Falcon for his contributions to the field of music.
On 16 May 1995 he was named a member of the Royal Swedish Academy of Music.