Darlington have been relegated four divisions to the Northern League Division One on the recommendation of the Football Association.
The Quakers had hoped to enter into the Evo-stik Premier having been told by the Football Conference they would not be admitted to its north section.
After going into administration this season, the club was advised it must agree to repay debts to creditors.
However no Creditors Voluntary Agreement was reached for those debts.
Subsequently the DFC 1883 Limited group purchased the club's assets from Darlington FC 2009 Limited.
That decision ensured the club, relegated from the Blue Square Bet Premier this season, could survive without repaying the debts, which remain with the existing holding company and not with the new group.
Among the teams they will face next term are FA Vase winners Dunston UTS and Shildon, with whom they ground-share.
"We had appraised all potential outcomes and have produced plans and a financial model that will work at this level," a statement from DFC 1883 Limited said.
"The focus now will be to get the football club back up through the leagues as quickly as possible.
"We can be inspired by clubs like Chester, Wrexham and others who have taken this journey and enjoyed great football, grounds with atmosphere and a rekindling of supporters' enthusiasm."
Now the club's immediate fate has been decided, moves can begin to replace former manager Craig Liddle, who agreed to join Sunderland as development coach.
"We expect to be able to name the new manager shortly," the statement continued.
"An excellent short list is in place, and now that we know which league we are in we can draw those discussions to a conclusion."