Kavanagh's departure from the board was announced on July 26 but it was made clear then he would continue as chief executive.
However, chairman Michael Slater has confirmed Kavanagh has now severed all connections with the Addicks.
A statement on the npower Championship club's official website said: "After we announced on July 26 that Steve had tendered his resignation as a member of the board of directors but that his employment as chief executive would continue, I received formal notice from him which terminated his employment.
"Change is inevitable in the management of any business and football is no different.
"Tony Jimenez, Richard Murray and I are looking forward to working with incoming executive vice-chairman Martin Prothero and have complete confidence that the executive and senior management team that he puts together will continue to build on the great progress we have made both on and off the pitch over the past year and half."
This latest announcement comes on the back of the earlier departures of Peter Varney and Alex Newall from the club's board.