The historic change took place two months before the anniversary of the former Labour leader's death from a heart attack at his London flat on May 12, 1994. Mr Smith had pledged to reform the party to make it electable after four successive General Election defeats to the Conservatives.
His widow, Elizabeth, had endorsed leader Ed Miliband's reforms before they were passed on Saturday.
Mrs Curran, the Glasgow East MP, yesterday added her voice to the feeling the vote was a fitting tribute to his commitment to party reform. She said: "These changes complete the work of John Smith and will mean the voices of ordinary people will be at the heart of our party. They will help us fulfil our party's historic mission of bridging the gap between people and power.
"There is now an opportunity for us to grow our movement across Scotland and reach out to people with the message that Labour offers real change."
Shadow Foreign Secretary Douglas Alexander made a similar point: "Twenty-one years after John Smith began this journey, Labour votes in favour of one member, one vote by 66.29% to 13.71%."
Labour leader Ed Miliband told the special conference in London it was "time to finish the unfinished business of John Smith" as he praised his party's "courage to change" by reforming rules on party membership, the link with unions and the way the leader is elected.
He told the audience of MPs, trades union leaders and other delegates he had taken a "big risk" when he put forward the reforms, but stressed: "I did not believe we could face up to the challenges the country faced if we didn't face up to the challenges faced by our party. You should be proud of the Labour Party that has shown the courage to change."
He said some people in Britain had felt Labour had lost touch with them, and they had been right, but he insisted: "These changes are designed to ensure this party never loses touch again."
But although it was a comfortable victory for the leadership, it was not always an easy ride with even union leaders who voted in favour of the changes making clear their bitterness about the handling of the Falkirk crisis.
The events which spiralled out of control and brought the Ineos petrochemical plant in Grangemouth to the brink of permanent closure started with local MP Eric Joyce throwing drunken punches in a Westminster bar.
Labour's search of a new candidate saw the Unite union pushing for one of their own, Karie Murphy to be selected and their tactics of signing up new members from the workforce at Grangemouth were questioned. Shop steward Stephen Deans was also constituency party chairman and he ended up resigning that post and being fired by Ineos amid union claims of a witch hunt.
At the special conference, Unite general secretary Len McCluskey said: "The report before us today starts to take us down the road of involving more trade unionists in the business of the party they support."
He received applause when he spoke of the sacrifice Mr Deans had made.
"The party has said it. The police - who should never have been involved - have said it and I am saying it again today: my union did nothing wrong.
"The smears and the lies will not deflect us from our political strategy but they do sometimes claim victims. That's why I would ask this conference to show its support for Stevie Deans, a decent working man, a loyal Labour member and trade unionist, hounded from his job by a boss who took advantage of our party's unnecessary arguments."