Trevor Birch, of administrators PKF, confirmed they have signed an agreement with the PST which is subject to receiving permission to sell Fratton Park.
The move comes after the administrators withdrew preferred bidder status from Portpin, the largest creditor in the Portsmouth Football Club (2010) administration, more than three weeks ago and named PST as the preferred bidders.
"We can confirm that we have signed a sale agreement with the PST to acquire the business of Portsmouth Football Club," Birch said in a statement.
"Portpin has rejected the Trust's offer for Fratton Park, so the sale has to be conditional on receiving the Court's permission to sell the ground. We are therefore in the process of submitting an application to the Court.
"I'm sure every member of staff, every player and every supporter will join with me in wishing to see a speedy resolution of what has been a protracted administration.
"Everyone involved in the transaction has worked incredibly hard to get the deal to this stage and, although there is still much that needs to be done, today's announcement marks what is hopefully the beginning of the end of the process."
If the deal goes through, it will be an interesting experiment in fan ownership of a well-supported English club.
Supporters' groups across Britain have been pushing for greater involvement in the running of clubs but few have managed to raise the money to match their ambitions.
"We hope to finalise the sale by Christmas and go into 2013 with a fresh start for our great club," said PST Chairman Ashley Brown.
"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," added Brown.
Some 2,000 Portsmouth fans had pledged two million pounds to help fund the takeover, PST spokesman Colin Farmery said, adding that the Trust would now start to collect the funds and look to other fans to back the deal.
Portpin said it was still interested in buying the club should the PST bid fail for any reason.
"We still believe our bid remains the best offer for the future of Portsmouth Football Club," Portpin said in a statement. "We remain ready to complete the deal in a matter of days, should the Trust be unsuccessful."
Portsmouth were in the Premier League as recently as 2010. They are now 18th in their 24-team division and have a 10-point penalty hanging over them for being in administration.