The takeover would bring to an end the tumultuous tenure of British-Iranian Moshiri, who first invested in 2016.
The sale is expected to be completed by the end of 2023, subject to Premier League, Football Association and Financial Conduct Authority approval.
The takeover would mean half of the 20 top-flight clubs are American-owned.
Moshiri said in a statement: “The nature of ownership and financing of top football clubs has changed immeasurably since I first invested in Everton over seven years ago.
“The days of an owner/benefactor are seemingly out of reach for most, and the biggest clubs are now typically owned by well-resourced private equity firms, specialist sports investors or state-backed companies and funds.”
777 founder Josh Wander said: “We are truly humbled by the opportunity to become part of the Everton family as custodians of the club, and consider it a privilege to be able to build on its proud heritage and values.
“Our primary objective is to work with fans and stakeholders to develop the sporting and commercial infrastructure for the men’s and women’s teams that will deliver results for future generations of Everton supporters.”
Everton lie 18th in the Premier League after picking up just one point from their opening four games this season.
They are in disarray both on and off the pitch, narrowly escaping relegation in the past two seasons, including staying up with victory on the final day last term.
Next month the club will go before an independent commission for an alleged breach of the Premier League’s Financial Fair Play rules, but Everton have denied wrongdoing and said they were “prepared to robustly defend” their position.
In March, the club posted financial losses for the fifth successive year, taking their cumulative losses over that period to more than £430m.
They are also in the process of building a new stadium on Bramley-Moore Dock and costs could reach £760m, a £260m increase on figures quoted by the club last year.
“I have been open about the need to bring in new investment and complete the financing for our iconic new stadium at Bramley-Moore Dock, on the banks of the Mersey, which I have predominantly financed to date,” said Moshiri.
“I have spoken to a number of parties and considered some strong potential opportunities. However, it is through my lengthy discussions with 777 that I believe they are the best partners to take our great club forward, with all the benefits of their multi-club investment model.”
Wander added: “We are committed to partnering with the local community over the long term, working on important projects such as the development of Bramley-Moore Dock as a world-class stadium venue, allowing thousands more Evertonians to attend our home matches and contribute to the economic and cultural regeneration of Merseyside.”
