The trust claims to have raised £3m in pledges, with £1m already collected in deposits, but requires a bridging loan in order to fund a £2.75m offer to buy the club from current owner Balram Chainrai.
The Portsmouth City Council voted unanimously to award the trust the loan with certain conditions attached. The club owned by the trust must be the same club that was relegated and operate in the Football League, ruling out the possibility of supporters forming a new club with the loan.
The PST must also obtain the remaining £11.7m to be paid in parachute payments, part of which will be used to pay back the council, as well as assets such as Fratton Park.
The council voted unanimously to award the loan, noting the impact the loss of the club could have on the local economy.
"I really thought it was going to be a tight vote and I’m so happy it was unanimous," Mick Williams, board member of the PST, said.
"This was real community support for a community club. Now Portpin know that we've got what it takes and they can't ignore us.
"The ball is in their court now. We've made an offer and we just have to wait and see."Leader of the council Gerald Vernon-Jackson added: "This has been a difficult decision, but if the council does not offer PST a loan then it is likely Portsmouth Football Club will not survive.
"This is a loan, not a gift or a blank cheque. The council will borrow the money and PST will have 13 months to repay us in full, with interest. No services will be affected as the money will not come directly from the current council budget.
"The financial impact of the football club on the city is huge. Livelihoods depend on the club surviving and thriving. The community projects the football club runs are hugely important to encouraging young people and supporting their potential and helping them through difficult times."