Dan Friedkin, owner of Italian outfit Roma, had initially agreed a deal back in June to purchase the Toffees, but talks gave way.
Miami's 777 Partners, who previously held interest in Everton, saw a deal collapse earlier this year.
John Textor, co-owner of fellow Premier League club Crystal Palace, was also given a period of exclusivity to hash out a deal with Moshiri.
That, too, bore no fruit and a statement released by Everton confirmed an agreement had been reached.
"Blue Heaven Holdings and the Friedkin Group confirm that they have reached agreement over the terms of the sale of Blue Heaven Holdings' majority stake in Everton Football Club," it said.
"The transaction is subject to regulatory approval, including from the Premier League, the Football Association, and the Financial Conduct Authority."
A spokesman for the Friedkin Group said: "We are pleased to have reached an agreement to become custodians of this iconic football club.
"We are focused on securing the necessary approvals to complete the transaction. We look forward to providing stability to the club, and sharing our vision for its future, including the completion of the new Everton Stadium at Bramley-Moore Dock."
The Group have already given the Blues £200 million to repay a loan and put working capital into the club.
A stumbling block in their initial purchase attempt was legal action 777 Partners faced in the US, according to the BBC.
Alongside the Friedkin Group and Textor, two businessmen local to Liverpool, Andy Bell and George Downing, were also said to be keen.
