Davis was born in County Dublin. His father was a Protestant and his mother a Catholic from Bray, County Wicklow. Davis attended a Catholic boarding school in County Antrim and describes his upbringing as ecumenical. During his childhood he acquired his love of boats which later provided the inspiration for the TV series Out of the Blue.
Davis started as a news reporter with the American network ABC and BBC Northern Ireland before spending 11 years in the newsroom in RTÉ. In the early 1980s he became a newsreader for The Six-o-clock News and began to become well-known due to his sometimes off-the cuff comments on news stories.
In the mid-1980s Davis co-hosted (with Thelma Mansfield) an afternoon show on RTÉ 1 called Live at 3. This led to him hosting his own talk show, Davis at Large in 1985. It was on this show, which was screened live, that he was attacked and hurled across the studio by a guest female body builder. In addition to this he had an interactive summer current affairs show, simply called Davis.
Davis presented the Rose of Tralee on one occasion in 1995 when Gay Byrne was taken ill at short notice. Live at 3 came to an end in 1997. Nearly 15 years later, Thelma Mansfield said, "They wanted to get rid of the old faces and bring in some new ones". Davis returned to the screen in the late 1990s with a marine programme devoted to boats and the waters around Ireland called Out of the Blue, which ran for four series, the last of which was broadcast in 2001.
In 2005, he hosted a show called Time on Their Hands, a travel series for older people. His latest television appearance was on the second season of Celebrity Bainisteoir, in which he and seven other Irish celebrities managed an intermediate club gaelic football team from their home county in an official GAA tournament. Davis's team won the tournament. He and eventual runner-up Katherine Lynch appeared together on Tubridy Tonight the evening before the final was broadcast. Clips from Davis's work as both RTE journalist and Live at 3 have been playfully riduled by the RTE sketch show The Savage Eye.
In 2000, Davis presented a radio quiz show called A Question of Food. During the summer season he has taken over RTÉ Radio 1's mid-morning slot usually occupied by Today with Pat Kenny, and he also hosted the radio phone-in show, Liveline, when regular presenter Joe Duffy was on holiday.
He currently presents Sunday Magazine with Davis on 4 on 4fm.
Davis has won two Jacob's Awards for his television work. In 1984, he received his first award for the series The Season That's In It. He won his second award in 1991 for his co-presenting of Live at Three.