He was born in Dublin and was educated at Blackrock College and University College Dublin, where he received a master's degree in Modern History. He worked as a secondary school teacher from 1991 until 1997. While still a teacher, he studied law at King's Inns and qualified as a barrister in 1997. His brother David McSavage is a comedian and his first cousin is Irish television and radio presenter Ryan Tubridy.
Andrews was first elected to public office in June 1999, when he was elected to Dún Laoghaire-Rathdown County Council. He was elected to Dáil Éireann at the 2002 general election. Andrews comes from a family with strong political connections. His grandfather, Todd Andrews fought in the War of Independence and became a founder-member of Fianna Fáil, while his grandmother, Mary Coyle, was a member of Cumann na mBan.
Andrews's father, David Andrews served as a TD from 1965 to 2002 and is a former Foreign Minister, while his uncle, Niall Andrews, was a former Fianna Fáil TD and MEP and his cousin Chris Andrews (son of Niall Andrews), is a former TD.
In June 2006, Andrews led a group of Fianna Fáil backbenchers in an unsuccessful attempt to establish a backbench committee to influence Government Policy. At the 2007 general election, Andrews retained his seat in Dún Laoghaire with 8,587 votes.
Andrews was appointed as Minister for Children and Youth Affairs in May 2008. As Minister, he framed the Government response to the Ryan Report on Institutional Abuse. This included an Implementation Plan that delivered an additional 200 social workers for the HSE Child and Family Services. In April 2009, Andrews introduced the Early Childhood Care and Education (ECCE) Scheme, which provided, for the first time, free universal access to pre-school education. The scheme continues to benefit 65,000 children annually.
After the release of the Murphy Report into child abuse in the Dublin diocese in November 2009. Minister Andrews, speaking at a conference in Dublin Castle, said it would be "amazing" if there were no consequences for people who were the subject of adverse findings in the report. Asked about the position of Bishop of Limerick Donal Murray, the Minister said:I think it's everybody's view that if adverse findings are made against an individual in a commission of inquiry then it would be amazing that there be no consequences for them.
Clearly pressure had been exerted from within the church on Bishop Murray, it would appear, and those consequences may come to pass.
He said he was also disappointed at the absence of a response from Rome.
He also introduced the Adoption Act 2010, which brought Ireland into compliance with the Hague Convention on Inter-country Adoption, providing new safeguards and standards.
On 31 January 2011, in the run up to the general election, Andrews was named Health spokesman by party leader, Micheál Martin
He lost his seat at the 2011 general election. For his eight years' service as a TD, Andrews is entitled to a lump sum of €110,312, a partial TD's pension between the ages of 45 and 49 (which he has not claimed), and beginning at age 50 a full pension of approximately €16,000 per year. He is entitled to a Ministerial pension of approximately €9,000 from the age of 65.
In May 2011, he returned to practising law at the Law Library, working mostly in areas of child law. In September 2012, he was appointed Director of Elections for Fianna Fáil for the Children's referendum.
On 8 November 2012, Andrews was appointed chief executive of aid charity GOAL, replacing John O'Shea. Andrews recently gave a TED talk titled, "Why No One Cares About Syria" in which he spoke about the alarming humanitarian situation in Syria and the international community's lackluster effort to address the problem. Andrews has traveled with GOAL to visit communities the organization assists. Andrews is also maintaining the strong connection to the Irish sports community that John O'Shea established when the organization was founded in 1977.