An overwhelming majority at the Grand Lodge quarterly meeting in Co Tyrone welcomed progress made through the joint plan from a DUP and Sinn Féin working group.
After a meeting of 120 members of the Order's Grand Lodge near Dungannon, Grand Master Robert Saulters said 95% voted to give the working group the space to continue working on the legislation.
However, it will not be in place for this year's marching season.
'We welcome the progress that has been made to bring legislation forward and publish a Bill and will make final comment when we see the Bill,' Mr Saulters said.
He added: 'We reaffirm our concerns on civil and religious liberties for all and regret the campaign to deprive people of the right to freedom of assembly.'
The Central Committee, which met on Monday, recommended that the order should give its tacit support for the proposed framework to resolve contentious marches. The proposal was passed without amendment.
The new framework for marches was devised by a six-man Sinn Féin/DUP working group that was set up as part of the Hillsborough Castle agreement last month. That group delivered its report to the office of the First and Deputy First Minister on 24 February.
The document is not due to be made public, which has concerned the loyal orders and residents' groups who oppose a number of marches in contentious areas.
The DUP's three representatives in the working group briefed the Order's Central Committee on Monday and it is understood the senior Orange representatives backed their proposals.
While details of the new management structures have not been made public, it is understood they are heavily influenced by a recent review of parades carried out by former Liberal Democrat leader Paddy Ashdown.
Central to those was the axing of the current Parades Commission adjudication panel, with more emphasis placed on achieving localised resolutions. The parades settlement is a key tenet of the Hillsborough Agreement.
The Grand Lodge meeting comes ahead of next Tuesday's crucial vote in the Assembly on the proposed timetable for law and order transfer.
