Mr Miliband proposed to end the automatic affiliation of union members to the party, which could cost Labour between £3-5 million, according to some estimates.
The changes were announced after Unite were accused of ballot-rigging in the selection of Labour's parliamentary candidate for Falkirk.
Mr Miliband said changing the party's relationship with the trade unions would end "machine politics".
Former Prime Minister Tony Blair hailed the move as "a real act of leadership" and admitted he should have taken the same step when he was in charge of the party from 1994-2007.
Unite's general secretary Len McCluskey, who last week said Labour had been "caught up in anti-union Tory hysteria" over the Falkirk controversy, welcomed today's proposed changes.
He said the plans were "visionary and in many ways could be historic" and added that he was "very comfortable" with the proposals, which he claimed could result in thousands more union members joining Labour.
Unite were accused of trying to fix the the selection of Labour's general election candidate in Falkirk by packing the constituency with 100 or more of its own members, some of them without their knowledge.
An internal party report on the allegations has been handed to police.
Mr Miliband said the Falkirk controversy represented "part of the death-throes of the old politics", and he hoped to usher in an "open, transparent and trusted" system which would engage more union members directly in the party.
As well as plans to stop union members from automatically affiliating with Labour, Mr Miliband announced he would establish a code of conduct for would-be election candidates and introduce primary elections for the party's next candidate for London mayor.
He also called on other parties to help him "clean up the way we finance our politics".
However, Conservative chairman Grant Shapps insisted that "nothing has changed" as a result of the speech.
"It's still the same old Labour Party with a weak leader in the pocket of the union bosses who's unable to stand up for hardworking people," he said.