The Glasgow-born businessman has agreed to pay close to £45 million to settle the long-running case.
But despite the sizeable payment, Mr King claims the deal will increase his capacity to invest in the Ibrox club, and ensure he passes any 'fit and proper person' test required by the Scottish Football Association.
Mr King said: "I regard the sum agreed as being very acceptable. It has no impact on my ability to invest in Rangers. In fact, the opposite is true.
"It means that there are now no restrictions on me whatsoever - plus the 'fit and proper' issue disappears as all fraud allegations were finally withdrawn by the state."
His words come as Greenock bus tycoon Sandy Easdale claimed to be the new largest shareholder after concluding a deal to buy the shares of former chief executive Charles Green.
Mr Green owned 714,285 shares in Rangers - about 7.7% of the total shareholding.
Normally, a significant share purchase would need to be swiftly announced by the company to the stock exchange, but Mr Easdale's spokesman Jack Irvine said it was a private deal Rangers had been unaware of.
The price agreed for the shares was also a private matter, he added.
The purchase by Mr Easdale, who owns McGill's Buses with his brother James, who has a seat on the board, adds to the 2.1% stake he acquired after buying 1.2 million shares from Imran Ahmad, a former director, two weeks ago.
In a statement, Mr Easdale said: "There has been continued speculation and constant inquiries to buy this largest holding in Rangers, but Mr Green gave me the first option, which I exercised. Between my family holdings and through other supporting investors, I now have the largest shareholding in Rangers Football Club."
The remainder of Mr Green's shares are due to go to Isle of Man-based investment firm Laxey Partners following a deal struck in June, his spokesman added.
The value of Rangers shares rose by 13% yesterday, finishing on 52p.
As news of Mr Easdale's deal emerged, Mr Green announced his financial interest in the club was now over. The chief executive, who left the club in April and returned for a short term as a consultant, said: "I want to make it clear that this means I will have no ongoing influence or financial interest at the club, but I remain a fan and fervently hope Rangers will soon be back at the top where they belong."
The rules of the AIM stock exchange, on which Rangers is listed, state a company must notify without delay any relevant changes to significant shareholders.
Mr Easdale's spokesman said it was likely the stock exchange would be informed next week of the May deal.