"We recently tried on a few occasions to remedy the situation between Mr Lorgat and the board, but we have not been successful in finding a satisfactory resolution," said Nenzani.
"The Board unanimously felt that it was in the best interest of the organisation that we agreed to a mutual separation agreement with Mr Lorgat."
Nenzani did not go into details about the breakdown in relations but it has been reported in local media that there were concerns about Lorgat's role in the setting-up of a new Twenty20 tournament, the Global T20 league, which is due to start in November.
CSA vice-president Thabang Moroe will take over as acting chief executive.
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Lorgat, 57, was appointed chief executive of CSA in 2013, initially on a three-year contract. His contract was extended until July 2019.
A chartered accountant and former first-class cricketer, Lorgat was treasurer of the then United Cricket Board of South Africa and was convener of the South African selectors before being appointed as chief executive of the International Cricket Council, a position he held from 2008 to 2012.
Lorgat has been the main driver behind the Global T20 League, which will consist of eight teams, including leading South African and international players. Seven of the franchise owners are from Asia, including Bollywood stars Shah Rukh Khan and Preity Zinta. No television deal has yet been announced.