King confirmed his planned departure had been completed in a personal statement on Friday night.
Douglas Park has been placed in interim charge of the board.
The South African-based businessman said: "At my final board meeting in Glasgow on March 14, the board was close to finalising a new round of funding, however this has been put on hold while the board considers the financial consequences of the rapidly evolving global impact of coronavirus.
"The subsequent severe developments within the sporting and general business environment – that have now resulted in global lockdowns – has necessitated that the careful financial planning assumptions presented on March 14 are revisited."
Rangers later announced John Bennett would be Park's deputy chairman and sought to reassure supporters over their finances.
A statement read: "RIFC is pleased to confirm that the funding plan announced at the recent AGM is well advanced, with significant investment already received and further commitments in place."
Rangers added that Bennett's "consistent investment in the club is set to continue, with further funding in the coming months".
Park said: "It is a privilege to take on this position at the world's most successful football club. We have experienced some difficult days but have emerged stronger than before.
"On behalf of the board of directors, I welcome the continued enthusiasm towards contributing to the future success of the company and club. We will make further public comment in due course."
Rangers forecast in November that they would need another £10million of funding before the end of the season after announcing an annual loss of £11.3million. King announced his intention to step down later that month.
Stuart Gibson, a Paisley-born, Japan-based businessman, has been in talks with Rangers over investing in the club.