Alagiah was born in Colombo, Ceylon. His parents, Donald Alagiah, an engineer, and Therese, were Sri Lankan Tamil. In 1961 his parents moved to Ghana in West Africa, where he had his primary education at Christ the King International School. His secondary education took place at St John's College, an independent Roman Catholic school in Portsmouth, England, after which he read politics at Van Mildert College, Durham University. Whilst at Durham, he wrote for and became editor of the student newspaper Palatinate and was a sabbatical officer of Durham Students' Union. He worked on South Magazine from 1982 until joining the British Broadcasting Corporation (BBC), where he was the Developing World correspondent based in London and then Southern Africa correspondent in Johannesburg.
In 2004, he returned to his grandfather's original home in Sri Lanka in the aftermath of the Asian tsunami to survey the damage. The family's former home had been destroyed, but he was able to recognise an old well where he had played with his sisters, although the well was unsalvageable.
Alagiah joined the BBC in 1989 after seven years in print journalism with South Magazine. Before going behind the studio desk, he was one of the BBC's leading foreign correspondents, reporting on events ranging from the genocide in Rwanda and the plight of the Marsh Arabs in southern Iraq to the civil wars in Afghanistan, Liberia, Sierra Leone and Somalia.
He was the presenter of BBC Four News from its launch in 2002; the programme was later relaunched as The World. In January 2003 he joined the BBC Six O'Clock News, which he co-presented with Sophie Raworth until October 2005, and with Natasha Kaplinsky until October 2007. Since 3 December 2007, he has been the sole presenter of the Six O'Clock News. Prior to that, he had been the deputy anchor of the BBC One O'Clock News and BBC Nine O'Clock News from 1999. Since 3 July 2006, he has presented World News Today on BBC World News and BBC Two, which was rebranded GMT on 1 February 2010. He is also a relief presenter on BBC News at Ten presenting mainly Monday to Thursday when Fiona Bruce is unavailable.
A specialist on Africa and the developing world, Alagiah has interviewed, among others, Nelson Mandela, Archbishop Desmond Tutu, former Secretary-General of the United Nations Kofi Annan and President Robert Mugabe of Zimbabwe. His other documentaries and features include reports on why affirmative action in America is a 'Lost Cause', for the Assignment programme, Saddam Hussein's genocidal campaign against the Kurds of northern Iraq for the BBC's Newsnight programme and a report on the last reunion of the veterans of Dunkirk.
In 2000, Alagiah was part of the BBC team which collected a BAFTA award for its coverage of the Kosovo conflict. He has won numerous awards including Best International Report at the Royal Television Society in 1993 and in 1994 was the overall winner of the Amnesty International UK Media Awards. He was appointed Officer of the Order of the British Empire (OBE) in the 2008 New Year Honours.
His appearances at literary festivals include Cheltenham, Keswick, Hay-on-Wye and London, and he has spoken at the Royal Geographical Society, the Royal Society of Arts and at the Royal Overseas League. He is on the Board of the Royal Shakespeare Company.
From 2002 to 2009, Alagiah was a patron of the Fairtrade Foundation from which in July 2009, he was obliged to resign by BBC Management who claimed professional conflict of interest. Complaints were received at the BBC from the public who were unhappy that Alagiah had been asked to step down. The BBC responded that in keeping with its principles of impartiality, it would be inappropriate for one of its leading journalists to be seen supporting a movement that clearly represents a controversial view of global trade. He has also been actively involved in supporting microfinance as a tool for development, including recent appearances in support of Opportunity International. He has been a patron of Parenting UK since 2000.
In 2010 he was given the Outstanding Achievement in Television award at the Asian Awards.
He is married to Frances Robathan, with whom he has two children, Adam and Matthew.
On 17 April 2014 it was announced that Alagiah was being treated for colorectal cancer. A statement from the BBC said: "He is grateful for all the good wishes he has received thus far and is optimistic for a positive outcome." On 28 June, Alagiah announced on Twitter that he was making "encouraging progress". Finally, on 28 October 2015, he announced that the treatment was officially over and he subsequently returned to the BBC on 10 November.