Pompey's prospective new chairman Iain McInnes hopes to be in charge in time for the January transfer window.
The agreement hinges on PKF receiving court permission to sell the club's Fratton Park ground, which is held as security by former Pompey owner and rival bidder Balram Chainrai.
Portsmouth have been in administration since February and have relied this season on loanees and players on month-to-month contracts, while they currently have coach Guy Whittingham in caretaker charge following manager Michael Appleton's move to Blackpool last month.
But McInnes hopes to get Pompey back on a secure footing in time to bring in some reinforcements in the new year.
''This truly is fantastic news and the start of a new chapter for Portsmouth Football Club,'' said McInnes in a statement on the PST's website.
''The hard work will continue during the court application process to ensure that we are in the best position possible to drive the club forward and build for the future ahead of the important January transfer window.''
PST chairman Ashley Brown added: ''We are thrilled and proud to have signed a sale agreement with the administrator to buy and run Portsmouth Football Club. We hope to finalise the sale by Christmas, and go into 2013 with a fresh start for our great club.
''This is a special day for the thousands of Pompey fans who have stood by their club and stood up to be counted.
''We thank everyone for their support so far, and look forward to many more Pompey fans joining us, and being part of history, as we create the biggest community-owned club in this country.''
Chainrai's company Portpin also released a statement saying they are still willing to take over the club if the PST's bid fails.
It read: ''We still believe our bid remains the best offer for the future of Portsmouth Football Club.
''We remain ready to complete the deal in a matter of days, should the Trust be unsuccessful.''