Friels was born in Kilwinning, Ayrshire, Scotland. His mother was a mill worker and his father a joiner. He lived in Kilbirnie until 1963, when his family moved to Australia, arriving in Darwin, Northern Territory before settling in the Melbourne suburb of Brighton. He worked as a bricklayer's labourer before studying at the National Institute of Dramatic Art (NIDA), and graduated in 1976 along with Linden Wilkinson and Michael Siberry.

Friels career began with work mostly in theatre and television. In 1980 Friels was a presenter on the long-running children's series Play School. His first film role was in the unreleased Prisoners (1981), starring with Tatum O'Neal. His first actual appearance in film was in Monkey Grip (1982), an adaptation of a novel by Helen Garner, where he starred alongside Noni Hazlehurst.

Friels has been married to Actress Judy Davis since 1984, and they have two children, Jack and Charlotte. They were briefly separated, but later reconciled. The relationship was briefly in the media when an argument led to a court order against Friels: however, they remained together at that time.

In 1986, he played the title role in Malcolm, about a shy mechanical genius, for which he was awarded the 1986 AFI Award for Best Actor. Friels was also nominated for the Best Actor award the following year, for his role in Ground Zero, but did not win: the film received mixed reviews, with one describing him as "a proficient enough actor, but...miscast". Friels later won another AFI Award in 1995 for his starring role in the 1994 Halifax f.p. telemovie Hard Corps. Friels has played a wide range of other roles. He was a megalomaniac corporate executive in the 1990 feature film Darkman.

From 1996 to 1999, he played Frank Holloway on Water Rats, a role which won him the Logie Award for Most Outstanding Actor at the 1997 awards. In his acceptance speech he said, "I'm very flattered for this and it's all rather silly, isn't it? So, thank you very much."

In late 1997, Friels was diagnosed with pancreatic cancer. However, his treatment was successful, and he is one of the very few victims of this disease to go into long-term remission. During his treatment he even continued to work on the set of Water Rats, until eventually the impact of the chemotherapy stopped him working, and he chose to have his character written out of the series by sending him on a sailing journey around the world. At this time, however, he also continued his stage work, and was performing in Sydney Theatre Company's Macbeth.

Since 2003, Friels has appeared as the main character in the BlackJack series of telemovies. In 2010 he also starred in Killing Time where he played notorious underworld figure Lewis Moran.