The £300 million sale has passed the Premier League owners and directors test after "legally binding assurances" that the Saudi state would not control the club were received.
The move can now go ahead after it was confirmed that the Public Investment Fund (PIF), which operates separately from the state, will provide 80% of funds.
A Premier League statement said: "The Premier League, Newcastle United Football Club and St James Holdings Limited have today settled the dispute over the takeover of the club by the consortium of PIF, PCP Capital Partners and RB Sports & Media.
"The legal disputes concerned which entities would own and/or have the ability to control the club following the takeover.
"All parties have agreed the settlement is necessary to end the long uncertainty for fans over the club's ownership.
"The Premier League has now received legally binding assurances that the Kingdom of Saudi Arabia will not control Newcastle United Football Club.
"All parties are pleased to have concluded this process which gives certainty and clarity to Newcastle United Football Club and their fans."
It is widely understood that Saudi Arabia settled a supposed piracy dispute with Qatar-based broadcaster beIN Sports and that has allowed things to progress.
The Saudi Arabian state has been accused of human rights abuses, but with the majority owner PIF deemed a separate entity, that, and any piracy issues, were no longer an impediment to the takeover, in the Premier League's view.
Amnesty International however have urged the Premier League to reconsider it's fit and proper persons test for club owners following the news.
In a statement they said: "Instead of allowing those implicated in serious human rights violations to walk into English football simply because they have deep pockets, we’ve urged the Premier League to change their owners’ and directors’ test to address human rights issues.
"Ever since this deal was first talked about we said it represented a clear attempt by the Saudi authorities to sportswash their appalling human rights record with the glamour of top-flight football.
"Saudi ownership of St James’ Park was always as much about image management for Crown Prince Mohammed Bin Salman and his government as it was about football."