Unite general secretary Len McCluskey has said he is delighted the union has been "vindicated" over Falkirk vote-rigging allegations.
Claims it tried to rig the selection of a party candidate led to a row with Labour leader Ed Miliband.
Labour has since decided no individual or organisation broke rules after evidence of wrongdoing was withdrawn.
Mr McCluskey told the BBC's Andrew Marr Show he welcomed Mr Miliband's plans to change the relationship with unions.
The row between Labour and its biggest financial backers looks set to dominate this week's TUC's annual congress in Bournemouth, which Mr Miliband is due to address on Tuesday.
At a press briefing, TUC general secretary Frances O'Grady said her advice was to "shake hands and move on" and predicted the Labour leader would get a "good reception".
Labour began seeking a candidate for the Falkirk seat when MP Eric Joyce announced he would step down at the 2015 general election after he was convicted of assault at a Commons bar.
It investigated allegations that Unite tried to sign people up as party members in the constituency without their knowledge to ensure the union's favoured candidate, Karie Murphy, was chosen.
The claims caused a row between Unite and Mr Miliband, who later proposed widespread changes to Labour's links with the unions.
Two union officials at the centre of the row have been reinstated, after Labour's investigation found no wrongdoing.
"Obviously we're delighted that we've been vindicated," Mr McCluskey said.
He said it was "time for us to move on from Falkirk and make sure that we are involved in uniting the party so that we can move forward".
Mr Miliband has said, nevertheless, he will press ahead with changes to Labour's relationship with the trade unions.
He has proposed union members should actively opt in to become individual full Labour Party members, instead of automatically becoming affiliated to the party as part of union membership.
An automatic "affiliation" fee - worth £8m a year to Labour in total - is currently paid by three million union members.
Mr Miliband's proposal prompted the GMB union to announce that, as of next year, it would cut the affiliation funds it gives Labour from £1.2m to £150,000.
It said there would also be cuts in spending on Labour campaigns.
Mr Miliband says changes will increase the number of active Labour members from the current 200,000 to "a far higher number".
Mr McCluskey said Unite welcomed Mr Miliband's proposals because "we don't agree with the status quo".
Asked how many of the union's members would join as individuals, he replied: "We'll have to wait to see."
He added: "Ed's hope is that tens of thousands, maybe hundreds of thousands, of ordinary trade unionists will now actively engage with the Labour Party.
"We certainly support that and we are going to be working enthusiastically to see if we can bring that about."
He said the challenge for Mr Miliband was "to make certain now that he demonstrates to ordinary working people, and indeed to organised labour, that the Labour Party is on their side".
The party must make sure it was "different to this Conservative government" and Mr Miliband must show that "the path to poverty that they have us on is something that he is going to oppose", he added.
Mr McCluskey later told BBC Radio 5 live's Pienaar's Politics that Mr Miliband had his support and the support of his party.
But he said: "He still has to close the deal with ordinary working people and this week, in Bournemouth, he has an opportunity."
GMB general secretary Paul Kenny was more critical in his comments, telling 5 live's Pienaar's Politics unions had been "demonised" during the row.
"I think the Falkirk thing, the manner in which the language that was used about trade unions was absolutely appalling and, if there is an apology owed, and I think there is, then the apology should be collectively to the trade unions," he said.
But Mr McCluskey insisted Unite was "not looking for an apology. We want to move on now - it's time to concentrate on the matters that matter to our members".
Mr Miliband's deputy, Harriet Harman, said he should not apologise to Unite, saying that "if serious allegations are made, it is the responsibility of the leader of the Labour Party to make sure they are properly investigated".
And Frances O'Grady, attending her first TUC annual congress since taking over as general secretary in the autumn, said she thought Mr Miliband would get a good reception when he makes his speech on Tuesday.
She added: "My advice is 'Shake hands and make up. Move on to the issues that really matter to working people.'"
However, Ms O'Grady added that unions would continue to ask "awkward questions this week".