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By David Deans
BBC Wales political reporter
Sir Kier Starmer has promised Wales control over its "economic destiny" by returning powers to Cardiff over the replacement for EU aid.
The UK Labour leader addressed the party's Welsh annual conference in Llandudno, Conwy county, on Saturday.
Sir Keir told party members Wales will "take back control" of the cash.
The Welsh government administered £375m a year on average when the UK was in the European Union.
The cash has been gradually wound down and will end this year, but the planned replacement - the Shared Prosperity Fund - is controlled by the UK government.
Councils bid for the cash and plan and deliver projects, but UK ministers said that would happen while "working closely" with the Welsh government.
The EU aid was part of a fund given to the poorest parts of Europe in an effort to boost their economies.
Labour ministers argued the system would give Wales less of a say and was an assault on devolution but the Conservatives claimed the Welsh government failed to make the most of the cash.
The Welsh government also said the plans fell short of promises to not leave Wales a penny worse off outside the EU, although that has been denied by the Treasury.
Labour did not provide details of how much cash would be provided to the Welsh government in the announcement.
Sir Keir told party members: "The argument is simple, the decisions which create wealth in our communities should be taken by people with skin in the game.
"The Tories have used the Brexit process to take back control of that money. Not from the EU - from Wales. It's an outrage."
He said "the next Labour government will return power over its economic destiny to Wales".
"The decision-making role for the Welsh government on structural funds, will be restored. It's time for Wales to take back control."
However Sir Keir managed expectations for how much public money might come from a future UK Labour government.
Warning that losing control of the economy would leave "working people" picking up "the bill," he said: "We can't let that happen - even when it puts a brake on things we might like to do in power.
"Sound money in our public finances must come first."
Sir Keir said opposition to the union of the UK in Wales was not "as advanced here as it is in Scotland".
But acknowledging Wales' independence movement, he said it should not be ignored "that it does find a voice in this nation as well".
To defeat it "comprehensively", he told Labour: "We need something else, we need hope."
Sir Keir set out a "clear choice at the next general election, between more decline and division with the Tories or credible change with Labour".
He promised that a Labour government after 10 years would have a stable economy with high growth: "There's more opportunity, more affordable housing, better paid jobs. Families feel they can get on, again, look forward with hope, again."
Later, Welsh first minister Mark Drakeford is expected to say that only a Labour government in Westminster can save the union of the United Kingdom.
He will say the union of the United Kingdom is "in peril as never before".
"Thirteen years of a party that has thrived on dividing our country, hurting the most vulnerable, striking at the institutions and the values that have bound us together - our openness, our generosity, our power to be a force for good in the world."