Neely was born in Belfast in 1959, graduated with honours in Modern History and English from Queen's University, Belfast. He began his career with the BBC in Northern Ireland in 1981. He covered the violence there for six years before joining BBC television in London.

After a brief period with Sky News, Neely joined ITN in 1989. During his time at ITN, he has covered many world events, amongst which have been the historic fall of the Berlin Wall that year, the breakup of the Soviet Union, the first and second Gulf Wars, the attack on the World Trade Center, the mass killings in the Darfur region of Sudan, the death of Pope John Paul II, the siege of Beslan, the Pakistan,China,San Francisco, Los Angeles,Assisi and Turkish earthquakes,the Asian Tsunami, the eruption of Mount Etna and numerous other natural disasters. For Beslan, Pakistan and the Tsunami,he was nominated for a prestigious Emmy award in the United States. Neely covered World Cups and an Olympic Games, numerous national elections and many international summits. He has won two Royal Television Society awards and received numerous other awards and nominations for international news reporting over the past decade.

Neely was Washington correspondent and U.S. Bureau Chief for six years (1991—1997), covering two Presidential elections, the bombings of the World Trade Center, the Atlanta Olympics and Oklahoma City, the OJ Simpson trial,the Waco siege as well as many major stories across North and South America and the Caribbean. From 1997 to 2002 he was Europe Correspondent, covering the death of Diana, Princess of Wales for which he was part of the team nominated for a BAFTA award; the crash of Concorde and the wars in Kosovo and Afghanistan. ITN received the Golden Nymph from the Monte Carlo Television Festival , Europe's top award for television journalism, for his work in Kosovo. He has also reported regularly from the Middle East.

On occasions, Neely can be seen as a presenter on various ITV News programmes.

He lives in Richmond, SW London with his wife, Marion, and two daughters, Sarah and Emma.