The decision paves the way for the former Walt Disney CEO to complete a summer takeover of the largest club under fan ownership in England, adding another colourful chapter to one of football's most famous old names.
"This is true fan ownership and democracy at work," PST chairman Ashley Brown said in announcing the result of the vote.
"We believe he (Eisner) understands the importance of the custodianship of Pompey and will be an owner all fans will be proud of."
Portsmouth, who were founded in 1898, have a gold-plated heritage, winning the title twice in 1949 and 1950, and the FA Cup in 1939 and 2008.
They have always enjoyed strong local support but a series of financial problems under foreign owners culminated in relegation from the Premier League in 2010, administration and further tumbles down the divisions.
With the club's future under threat, the PST took control in 2013 alongside 12 "presidents", nine of whom also now support selling to Eisner, after raising enough money from 2,750 members to secure a 48.5 per cent stake.
Eisner and his Tornante investment group have offered 5.57 million pounds ($7.25 million) for Portsmouth, matching the amount the supporters originally raised.
"Hoping to complete acquisition process (due diligence and all that stuff) this summer," California-based Eisner said on Twitter on Monday.
The decision to revert to outside ownership now has been controversial with not all supporters in agreement. But the 75-year-old Eisner topped up his bid with the promise of £10 million more investment, with at least £5 million earmarked for the repair of Fratton Park, Portsmouth's tumbledown ground on England's south coast.
"It seems to me that this would be an investment my children and grandchildren could participate in," Eisner said on a visit to the club earlier this year. "We are not doing it to have a failure financially, obviously, but that is not the only reason why we are doing it."
Around a third of English clubs are under foreign ownership. Premier League clubs Arsenal, Liverpool, Manchester United Swansea City and recently relegated Sunderland are all under the control of Americans, who increasingly regard English football as an attractive investment.
In 2015, Forbes magazine estimated Eisner's net worth at $1 billion.
(Reporting by Neil Robinson; editing by Mark Heinrich)
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