Johnston was born in Lindi, Tanganyika (present-day Tanzania), to Scottish parents, and was educated at the independent Dollar Academy in Dollar, Scotland. He went on to study at the University of Dundee, where he graduated with an MA in English and politics. Johnston also completed a diploma in Journalism Studies from Cardiff University.

Johnston joined the BBC in 1991, and has spent eight years as a correspondent for them, including in Tashkent, Uzbekistan, as well as Kabul, Afghanistan. He was in Kabul when Afghanistan was still under the control of the Taliban. He was due to be the BBC's full-time correspondent in Gaza until 1 April 2007, and at the time of his kidnapping was the only foreign reporter with a major Western media organisation to still be based in the city.

Johnston covered many major stories in Gaza for the BBC, including Israel's unilateral disengagement plan in 2005, Hamas winning the 2006 legislative elections, the 2006 Israel-Gaza conflict and the Palestinian factional violence of late 2006 to 2007.

Johnston is regarded by the BBC as a respected, experienced journalist, and due to his local knowledge, he was someone other journalists would turn to for information when in Gaza. Prior to being kidnapped however, Johnston was not a journalist well known to the general public. Following his release he announced his intention to return to obscurity though, as of January 2008, he took over the presentation of the BBC World Service version of the programme From Our Own Correspondent.

Johnston's BBC colleague Paul Adams noted that it was Johnston's "job to bring us day after day reports of the Palestinian predicament in the Gaza Strip." Mustafa Barghouti, Palestinian Information Minister, has described Johnston as a "friend of our people", and said that Johnston "has done a lot for our cause." Imprisoned Fatah leader Marwan Barghouti has also called Johnston a "friend of the Palestinian people".

When not working as a correspondent, Johnston produces radio reports, one of which, on life after the Taliban, won a Sony Radio Academy Award bronze. Johnston has also worked as programme editor of The World Today and as a general reporter in the BBC World Service newsroom.

The London Press Club named Johnston as British Broadcasting Journalist of the Year at an awards ceremony held on 10 May 2007. Accepting the award for Johnston, who was spending his 60th day in captivity, his father said that while the award meant a lot, "my family ... would like Alan to stand here today himself."

The day after he was released, Johnston was awarded a prize by Amnesty International for his radio reports on human rights in Gaza, praising him for his "commitment to telling ordinary peoples' stories."

On 12 March 2007, Johnston was kidnapped by the Army of Islam. His captivity led to many protests worldwide. Hamas put immense pressure on the Army of Islam, including (according to a senior Hamas militant) the threat to hunt them down and kill them if they didn't release Johnston. On 4 July 2007, Johnston was freed. He was taken to meet Hamas leader Ismail Haniyeh before leaving with an entourage of British diplomats to Jerusalem.

On June 19, 2008, the University of Dundee conferred an honorary degree of Doctor of Laws upon Johnston.