Fergus Linehan, 43, a former artistic director of both the Sydney Festival in Australia and the Dublin Theatre Festival, said he respected the EIF's traditions.
He said he would balance change with the knowledge the event is "not a blank canvas", and that he looks forward to moving to the city.
Mr Linehan, whose experience includes running not only festivals but also theatre, contemporary music and digital art, will succeed Jonathan Mills, whose final festival will be next year, and will run the festival until at least 2019.
Mr Linehan, whose mother is actress Rosaleen Linehan, lived in Edinburgh in 2009 when his partner, Sophie Hodges, worked in the festival's press office.
He increased the financial turnover at the Sydney Festival, increasing its ticket sales and commercial sponsorship and, as head of music at Sydney Opera House, he revamped its year-round music programme.
He is also festival director of Vivid Live, an annual event at Sydney Opera House which champions pop and digital art.
Mr Linehan will be director- designate, on a part-time basis, from May 1, to allow him time to plan his first full festival in 2015 and will become director and chief executive from October 1.
He said his new post was the one that "towers over them all" and he was "deeply honoured".
He said: "The job is a very interesting one, because the festival is not a blank canvass.
"People care deeply and have a sense of ownership. I need to begin a lot of conversations, to find the responses of the city and the festival.
"You want to win the public's trust, particularly in Edinburgh, which has such a strong history: but at the same time, people do expect you to progress."
His father, also called Fergus, is a novelist and playwright who was arts editor of The Irish Times. Older brother Hugh is features editor of The Irish Times, while his younger brother, Conor, is a concert pianist.
Mr Linehan said he would try and strike a balance between international and Scottish work at the annual event.
At the Dublin Theatre Festival he commissioned work by artists including Seamus Heaney, Brian Friel and Roddy Doyle as well as other Irish writers and choreographers. While there he also presented EIF productions such as Measure for Measure directed by Luc Bondy and Calixto Beito's Hamlet.
He said: "There is an endless debate of how you develop national and international work and it is about striking that balance."
Mr Linehan, who studied at University College Dublin, is director of Warehouse Arts, a company that provides artistic programme and planning services to a range of arts organisations around the world.
He will move to Edinburgh in 2014 and is currently in Australia, where his partner is expecting their first child in May.
Donald Wilson, Edinburgh's Lord Provost and chairman of the Edinburgh International Festival Society, said: "Fergus brings new skills, intellectual rigour and a highly successful track record to the festival and the city.
"Having previously lived in Edinburgh and worked with companies visiting the city he is familiar with what the city can offer its residents as well as visitors and artists from around the world."
Mr Mills said: "I congratulate Fergus on his appointment."