The former Sheffield United chief executive now needs the support of other SPL sides before his club will be admitted to the top flight.
Regulations require two weeks notice to be given before holding a general meeting, where SPL clubs will vote on the issue, so July 2 is the earliest date that a general meeting can be convened for the newco vote.
All 12 member clubs need to vote on this application and eight votes are required for Rangers to be playing SPL football next season.