Portsmouth's administrators PKF on Thrsday confirmed they were considering a bid fronted by football financier Harris.
But the Football League responded by announcing the troubled club, who have been in administration for almost a year, would be thrown out of the League if the Trust - PKF's preferred bidder - is not successful.
PST chairman Ashley Brown said in a statement: "The Football League has come to a sensible decision.
"Our bid is ready to go and we will be meeting with the administrator PKF shortly to prepare the timetable to complete our takeover.
"We have always been clear we are the best solution for the creditors and the best solution for the club and this has now been recognised across the board.
"Our bid will put capital into Portsmouth FC and will make a clean break from the past.
"Any fans who have been unsure about backing our bid financially can now do so in the confidence their money will go towards the rebuilding of the club.
"There is no knight, white or otherwise, who is going to do it for them."
The PST's bid hinges on being able to buy the club's Fratton Park ground, which is controlled by former Portsmouth owner Balram Chainrai. PKF are seeking permission to sell the ground and are due in court with Chainrai's company Portpin next Thursday.
- Sports & Recreation