Lorgat, 47, will take over from the current CEO, Malcolm Speed, following the ICC Annual Conference, scheduled to take place between June 29 and July 4, an ICC press release said.
Lorgat's appointment, comes days after Imtiaz Patel, another South African, turned down the ICC's offer and follows a meeting he had with David Morgan, the ICC's president-elect, in Pretoria on Wednesday.
The appointment was approved by the ICC's recruitment board, comprising Morgan, the ICC president, Ray Mali, the vice-president, Sharad Pawar and Creagh O'Connor, the chairman of Cricket Australia.
Lorgat said he look forward to an "exciting and rewarding journey in a game I have truly loved from a very young age."
He takes over at a time when the game, and the ICC, face several difficult decisions. "I am under no illusion about the challenges that await me, but those challenges are also opportunities and I cannot wait to start work at the highest level in such a great game."
Mali expressed his delight at Lorgat's appointment. "I have worked alongside him for a decade in South African cricket and I have seen first-hand what a great team player he is and that is something that will serve both him and the game extremely well in the years to come."
Lorgat previously held several posts in cricket administration. He was chairman of Western Province Professional Cricket and a board member at Western Province Cricket Association.
He also served as a finance committee member for the United Cricket Board of South Africa (UCB) (1999-2004), was a member of the ICC's World Cup finance committee (2000-2003), was a board director and treasurer of CSA (2003-2004) and a selector (2001-2003). In 2004, he was appointed as chairman of selectors for CSA, a position he held until 2007.