Hartung was born in Maryborough, Queensland in 1948. His father was a hairdresser and mother was a nurse.
His father died in 1950 from a war related illness and mother died when he was 14. In 1959, Hartung's mother and two siblings had located to Wellers Hill in Brisbane. Hartung attended Mary Immaculate Primary School, Annerley, St James College, Brisbane and St Laurence's College. Hartung was dux of his class in his final year at St Laurence's College and captain of the First XV rugby union team, which were joint premiers. Legacy Australia supported him to complete his schooling.
In 1970, Hartung completed a Bachelor of Arts degree and Diploma of Journalism at the University of Queensland. He has a Master of Arts from the University of Sydney and his thesis examined the impact of lobbying on Australian Government's decision making process.
His wife Maureen is Executive Director of the Blue Gum Community School in Canberra. His son Michael is the general manager of Sport at the Australian Paralympic Committee and was appointed Chef de Mission for the Australian Paralympic Team at the 2010 Winter Paralympics in Vancouver, Canada. His daughter Catherine, recently completed a PhD in children's rights at the University of Wollongong.
In 1972, Hartung was employed as a cadet at the Courier Mail. In 1973, he joined the Australian in its newly opened Brisbane Office as a graded journalist. He was employed as a sports journalist in Sydney and London. In 1975, he took up a position as a political correspondent for The Australian in Canberra.
In 1975, he worked as a political journalist in Canberra and during this time, Hartung wrote several newspaper articles highlighting the inadequate support from the Federal Government for sport and assisted John Brown, Shadow Minister for Sport, to develop the Australian Labor Party's sport policy for the 1983 Federal Election. He wrote a chapter titled Sport and the Canberra Lobby for the book Sport : money, morality and the media. In 2014, he was appointed adjunct professor of sport at the University of Canberra and will be involved in the new Master of High Performance Sport course.
Hartung was appointed a member of the Interim Committee of the Australian Sports Commission (ASC) established by Minister for Sport, John Brown in early 1983. In 1984, he was appointed general manager of the Australian Sports Commission, a position which he held until 1988. During his period as general manager, the ASC developed programs in sport participation including Aussie Sport and high performance support for athletes. In August 2006, he was appointed to the Board of the Australian Sports Commission and in November 2008 was appointed chairman, a position which he held until his resignation on 4 April 2010. He resigned due to increased International Paralympic Committee commitments. Minister for Sport, Kate Ellis paid tribute by stating "Mr Hartung is a leader in national and international sports administration and we're fortunate to have benefitted from his talents over many years. Mr Hartung's dedication to sport, and particular achievement in promoting elite sport for those with a disability, has contributed to a well-run and inclusive sporting environment in Australia". Whilst on the Board, he was Chairman of the Australian Sports Foundation.
From 1989 to 1995, Hartung was President of the Confederation of Australian Sport, a peak sport body with the objective of providing a united voice in negotiations with government and stakeholders. As President, he argued that all minor sports deserved support due to the Australian Sports Commission's mandate of sport being for all Australians. He was made a life member of the Confederation.
Hartung was President of the Australian Paralympic Committee from 1997 to 2013 Hartung served as the President of the South Pacific Paralympic Committee. He also established the Oceania Paralympic Committee, and served as the Deputy President of the Sydney 2000 Paralympic Games Organizing Committee. Peter Dutton, Minister for Sport made the following comments about Hartung after his resignation as APC President.
Greg has made a significant contribution to the national and international Paralympic movement and has helped to increase support and respect for athletes with a disability. He has overseen the Australian team's preparations for eight successful Paralympic Games. In fact, the Australian team has not finished outside the top five in the medal tally at the Summer Paralympic Games during Greg's tenure, with Australian athletes earning 85 medals at the London 2012 Summer Paralympic Games. Greg helped to introduce world-class national programs in classification and talent identification, and improved the pathways for athletes with higher levels of disability to transition from community sport to the national team.
On 23 November 2009, Hartung was elected the Vice-President of the International Paralympic Committee Governing Board at a meeting of the IPC General Assembly in Kuala Lumpur. He is the first Australian to become a Vice-President of the IPC. He is a member of the International Olympic Committee Co-ordination Commission for the 2016 Olympic and Paralympic Games and a member of the International Olympic Committee Radio and Television Commission. Hartung did not seek re-election in the 2013 IPC Governing Board election.
Hartung owned the company Access Communications. This company specialised in publishing, political monitoring and databases. Hartung sold Access Communications to CCH in 2000. He currently the Company Director and Principal of GNH Management. He is a graduate of the Australian Institute of Company Directors.
Hartung has been recognised for his work, receiving several awards including:2013 – Officer of the Order of Australia (AO)
2008 – Inaugural Life Member of the Oceania Paralympic Committee
2002 – Medal of the Order of Australia (OAM)
2001 – Centenary Medal
1996 – Life Member and Fellow of the Confederation of Australian Sport