Speaking at he club's AGM in Glasgow, King confirmed his decisions with rumours circulating that he would do so prior to the event.
He will step aside in 2020, noting that this was his final AGM.
His announcement was met with a standing ovation.
He said: "However, as I highlighted earlier, the crisis is now finally behind us and normal activities can resume. In order to have smooth succession planning I therefore advised the Board last month that this will be my final AGM. The hard work of recovery is now done and I intend to step down from the Board in the new year as soon as the new funding round has been concluded by the sub-committee and the new devolved operating structure for the Club that was approved yesterday has been fully implemented. I estimate that will take about four months.
"I now look forward to paying more attention to my South African and international businesses and to finally having the time to work with my children in the manner I had intended before my duty to Rangers put that plan on the backburner. The South African economy is very tough at the moment and it is time that I redirected much more of my attention to my private affairs.
"I would not step down if the Club continued to need my services and support. But it doesn’t.
He added: "I thank all of our shareholders and fans for the absolutely magnificent support I have received. Despite the personal trials and tribulations, I want to state that being the Chairman of Rangers has been, by far, the greatest privilege of my business life and I will continue to use my shareholding influence to support the Club and its board."
King will remain on the board of Rangers Retail LTD until their legalissue with Sports Direct has come to a conclusion.
He said: "I will also continue to represent Rangers on the board of Rangers Retail Limited until conclusion of the litigation with Sports Direct, however long that takes."
The Scottish-born, South African businessman first became involved with the club back in 2000 as a non-executive director.
In January 2015 he became the club's largest sole shareholder after his company bought 15 per cent of the club.
Later that year his consortium won control of the Ibrox board room and he was appointed the club's chairman.