Tony Blair has backed Ed Milband's proposed reforms
"Today, we won't just be voting to open our doors. We'll be voting for the biggest transfer of power in the history of our party to our members and supporters," he said.
Mr Miliband won the last leadership election largely thanks to support from unions, but Unite boss Mr McCluskey said he suspected only 10% of its one million members affiliated to Labour would opt to stay in if they were asked now.
An estimated 400,000 Unite members do not vote Labour - a situation Mr McCluskey said was untenable.
Members from the Trade Unionist and Socialist Coalition, which is not affiliated with Labour, have been holding a demonstration against the changes outside the centre.
Labour leadership elections are decided by a complex electoral college system, with equal weight given to the votes of three groups - one third to MPs and MEPs, one third to ordinary party members and one third to trade unionists.
Mr Miliband said a "one-member, one-vote" system would breathe new life into the party and complete a process started by former leader John Smith more than 30 years ago.