Morrison was born in the town of Rotorua, in the North Island of New Zealand, the son of Hana and Laurie Morrison, a musician. He is of Māori, Scottish, and Irish descent.His sister was performer Taini Morrison and his uncle was musician Sir Howard Morrison.
He has an adult son, James, from a relationship in the late 1980s with singer Kim Willoughby from the all-girl group When The Cat's Away.
His secondary education took place at Wesley College, Auckland.
Morrison lives in New Zealand, and divides his time filming there and in Australia and the United States.
Trained in drama under the New Zealand Special Performing Arts Training Scheme, one of his earliest roles was in the 1988 film Never Say Die, opposite Lisa Eilbacher. Before this he played Dr. Hone Ropata on the television soap opera Shortland Street from 1992–1995; he was immortalized when another character rebuked him with the line "You're not in Guatemala now, Dr. Ropata!"
In 1994 he received attention as the violent and abusive Māori husband Jake Heke in Once Were Warriors, a film adaptation of Alan Duff's novel of the same name. The role won him international acclaim, and he received the 1994 award for best male performance in a dramatic role from the New Zealand Film and TV Awards. He reprised the role in the sequel, What Becomes of the Broken Hearted?, for which he received the Best Actor award from the New Zealand Film Awards. He has appeared in supporting roles in Speed 2: Cruise Control (1997) and The Beautiful Country (2004). In 2005, Morrison became the host of the talk show The Tem Show on New Zealand television.
He has an adult son, James, from a relationship in the late 1980s with singer Kim Willoughby from the all-girl group When The Cat's Away.
