NI First Minister Arlene Foster said she was shocked and deeply saddened to hear of Mr Hunter's death.
He was well-known to the public as a television and radio reporter with the BBC in Northern Ireland.
He later was appointed as director of media and public relations with the Royal Ulster Constabulary.
Mr Hunter, 64, had also served in a senior role in the BBC Northern Ireland press office.
In a statement, the Hunter family said they were "absolutely devastated at the loss of a loving husband, father and grandfather".
Mrs Foster said Mr Hunter was "held in the highest regard by all who knew him".
"As a highly respected journalist for many years, Austin's professionalism and exemplary journalistic skills put him at the forefront of his profession," she said.
"Austin was a man of deep integrity and objectivity who was respected by all who knew him or came in contact with him."
Deputy First Minister Martin McGuinness described him as a "very good journalist and nice man".
"Austin was a man with a wide range of communication and interpersonal skills and made a considerable contribution to the media and public relations industry here for over 40 years," he said.
Ulster Unionist Party leader Mike Nesbitt, who worked as a journalist with the BBC and UTV, said Mr Hunter was a "great journalist" and "superb human being".
Mr Nesbitt said Mr Hunter had been "very encouraging" when he began his career at the BBC.
Peter Johnston, director of BBC Northern Ireland, said Mr Hunter was "a true professional".
"He demonstrated his great skill as a journalist on the frontline of reporting of some of the toughest times in Northern Ireland and throughout his BBC career he also gave generously of his time and knowledge to encourage others," he said.
Former colleagues of Mr Hunter at BBC Northern Ireland and across the media have also paid tribute.
Kathleen Carragher, Head of BBC News NI, said her former colleague was "passionate about Northern Ireland, the people and the politics and it informed all his work".
"He helped many young journalists in Northern Ireland develop their careers and he will be deeply missed by all who knew him."
Former Controller BBC Northern Ireland Anna Carragher said Mr Hunter was "a very sensitive man who was also fantastic fun to work with".
Andrew Colman, former head of news and current affairs at BBC NI, said Mr Hunter had reported on "many of the most difficult and challenging circumstances" of the Troubles "with great compassion and integrity and won the respect of all".
Former head of news and current affairs and chief editorial adviser BBC NI, Keith Baker, said Mr Hunter was "always calm and measured and was trusted by audiences and by those he had to work with on stories, particularly those who were recently bereaved".
"He will be remembered for his honesty, for being a great colleague and mentor and for that impish sense of mischief that was never far away."
News Letter editor Alistair Bushe said Mr Hunter's leadership skills had helped "lead it out of a difficult period", adding that he had maintained an affinity for the newspaper.
Head of the Police Service of Northern Ireland's corporate communications department, Liz Young, said Mr Hunter had "brought a wealth of skill, professionalism and experience to the organisation".
In recent years, Mr Hunter had travelled around the world sharing his expertise with other countries.
He was in Bahrain working for the not-for-profit organisation Northern Ireland Co-operation Overseas (NI-Co) when he died.
NI-Co chief executive, Graeme McCammon, said Mr Hunter was a "highly-valued member of the team".
"We will remember him for his outstanding talent, principles, compassion and his commitment to change," he said.
"Austin was recognised and respected worldwide as an expert in his field and his knowledge and opinions were greatly valued by all who knew and worked with him."
Mr McCammon said Mr Hunter had been in Bahrain advising on the implementation of youth justice reforms.
Mr Hunter also worked as a consultant with the Orange Order from 2006 to 2012, advising it on media relations.
Grand Master Edward Stevenson said: "As well as being an absolute gentleman and an individual of the utmost integrity, Austin was a colossus in the field of journalism and public relations."
The former BBC journalist and News Letter editor Austin Hunter has been killed in a traffic accident in Bahrain.