Mr Andrews, a former Children's Minister, will take over the charity following the resignation in August of John O'Shea -- who founded the charity in 1977.
He was one of 88 applicants from 18 countries to apply for the position, which was publicly advertised, and was selected by an independent panel.
"I have a strong affinity with the work that GOAL do and know about the ethos from my sister (who worked for GOAL in Calcutta)," Mr Andrews said said.
He attended one informal and two formal interviews for the job -- the final one chaired by independent panel member senator Martin McAleese.
"They asked me to outline a strategy for the first few years and I gave them my vision," he said.
A GOAL spokesman refused to reveal the remuneration package. While Mr O'Shea never talked about the amount he was paid, it was revealed in 2010 that he was on a salary of €98,320.
Mr Andrews's junior ministerial colleague in the last government, Peter Power, has also made the move to aid organisations.
Mr Andrews said he was "very excited to be chosen" and was looking forward to the challenge. His plans include:
• Implementation of best practice in corporate governance.
• Stabilisation of fundraising "to build on the success of the past".
Mr O'Shea's resignation came after controversy over a decision to take out a court injunction preventing the board of the organisation from dismissing him.
The former charity boss rejected complaints of "institutionalised bullying" in court as "false and concocted" when applying for the injunction.
However, he stepped down and agreed to take an "ambassadorial role" in the charity.
Mr Andrews said yesterday he would contact Mr O'Shea to discuss the role when he starts in the coming weeks.
Welcoming the appointment, GOAL board chairman Pat O'Mahony said the organisation would grow and remain true to its ethos to deliver aid to the poorest of the poor.