The League are now awaiting the outcome of this week's make-or-break High Court hearing over the sale of Fratton Park, and for the PST to raise the remaining funds as set out in their business plan, before fully considering their application.
PST chairman Ashley Brown said: "We are very pleased the Football League has shown confidence in our bid by endorsing our proposed membership. This is a highly significant moment for the club.
"We have always argued that Pompey needs a community-led solution and we are very pleased the League shares our confidence in our ability to turn the club around.
"Thanks to the backing of our fans and our individual investors we have a robust business plan, which the League has endorsed.
"We now need fans to back us financially to ensure our club survives. This is a landmark moment on the road to rehabilitating the club and we now need everyone who can to buy a share or convert their pledge as soon as possible. This will ensure we are in a strong financial position prior to the court case."
The Trust's bid, and Portsmouth's future, hinges on administrators PKF gaining permission to sell Fratton Park, which is controlled by the club's former owner Balram Chainrai, at the High Court hearing which starts on Thursday.
The League have also confirmed Pompey still face a 10-point penalty if and when they finally come out of administration, which is likely to leave them in the relegation zone.
Brown added: "Of course we are disappointed that the League has confirmed the points deduction, although the reasons for it are the fault of those who have mismanaged the club so badly in its recent past."