Andrews was first elected to Dáil Éireann at the 1965 general election as a Fianna Fáil Teachta Dála (TD) for the Dún Laoghaire and Rathdown constituency. From 1970 to 1973, he served as Parliamentary Secretary to the Taoiseach with special responsibility as Chief Whip.
Following four years in opposition Jack Lynch and Fianna Fáil were back in power in 1977, and Andrews was appointed Minister of State at the Department of Foreign Affairs. In the 1979 Fianna Fáil leadership election, Andrews supported George Colley, the favoured candidate of the existing leadership. However, Charles Haughey, in a very close vote, was elected leader and Taoiseach.
Andrews paid for backing Colley in the leadership bid, being confined to the backbenches during Haughey's thirteen-year period as leader. During this period, he maintained his legal practice and campaigned for the Guildford Four, the Birmingham Six, and Brian Keenan. He remained a vocal critic of Haughey during this period. After the Progressive Democrats were founded in 1985 Andrews considered joining the new party.
In 1992, Albert Reynolds replaced Haughey as Taoiseach and Andrews was briefly appointed Minister for Foreign Affairs, vacating this position to Dick Spring, Tánaiste and Labour Party leader, after a subsequent election. Andrews was then appointed Minister for Defence and the Marine. In 1997, subsequent to a general election, Fianna Fáil were back in coalition with the Progressive Democrats, with Bertie Ahern as Taoiseach. Andrews was first appointed Minister for Defence, subsequently, after the resignation of Ray Burke becoming Minister for Foreign Affairs.
His period as foreign minister was successful regarding the Northern Ireland peace talks. In April 1998, the Good Friday Agreement was adopted by the people of the Republic and Northern Ireland.
In 1999, Ireland joined the Partnership for Peace project. Andrews retired as Minister for Foreign Affairs in January 2000. He retired from Dáil Éireann at the 2002 general election, his son Barry was elected for the Dún Laoghaire constituency, his other son David Andrews, Jnr is a comedian who works under the pseudonym of David McSavage. His brother, Niall Andrews, was a TD and MEP. On retirement from politics, he was appointed Chairman of the insurance company, MGM International.
In May 2000, he was appointed to the non-executive position as Chairman of the Irish Red Cross Society, serving in that position until 2009.