The deal remains subject to a court case next month at which administrators PKF will attempt to gain permission to sell Fratton Park, which is controlled by former owner Balram Chainrai, to the fans' group.
Trust chairman Ashley Brown said: "We are delighted to announce that on Thursday afternoon we exchanged contracts with PKF for the acquisition of PFC. We must now focus on securing the release of the charge on Fratton Park, which in turn will trigger the completion of the deal."
He added: "We are on the verge of creating football history. Several thousand fans are already part of that and we urge others to now join us so that they too will own a part of their club.
"We are confident of success in the court, but we would still welcome the opportunity to settle quickly and allow us to start the job of rebuilding the club with the community and supporters at its heart."
Investor Iain McInnes, who will become Portsmouth's new chairman if and when the takeover is complete, added: "If you believe it you can achieve it. I'm proud to be part of a group of people who have collectively pulled together to get us this far.
"Finally the fans can see the end of what's been a very long and challenging haul.
"We will not be counting any chickens just yet, particularly as there's due process to go through. However, I believe that if a bid is to be judged on its merits - financially, operationally and motive - then there can be only one outcome. So let's get on and get this done."
Pompey have been in administration for over a year and will be deducted 10 points when they exit. The club are currently bottom of League One but won their first match in 24 attempts against Crewe last week.
- Sports & Recreation