In a speech tonight, Shadow Foreign Secretary Douglas Alexander will call for new powers on tax, elections and employment schemes to be handed to Holyrood if Scots vote to stay in the UK in September's referendum.
He will tell an audience at Glasgow University: "This radical approach is both right in principle and popular in practice.
"It is what most Scots want."
The call comes as Scottish Labour prepares to unveil the recommendations of its internal devolution commission, established to consider how best to increase Holyrood's powers, at a potentially rancorous conference in Perth next month.
The party remains deeply split on the issue with many MPs and some MSPs - including former finance spokesman Ken Macintosh - fiercely opposed to handing the Scottish parliament greater control over income tax, a move suggested by the devolution commission a year ago.
Mr Alexander's intervention is understood to have been backed by Scots Labour Johann Lamont and UK party leader Ed Miliband and will be seen as a bid to win over opponents and head off a threatened boycott of the Perth gathering by angry MPs.
He will say: "I believe Scottish Labour's devolution commission can and should embrace further devolution of powers within the UK and within Scotland.
"It should be a defining point in the debate, where a reckless and wrong White Paper is confronted by the right and radical way forward. I would encourage my colleagues in the Devolution Commission to range widely and act boldly."
Mr Alexander will call for greater devolution of tax to "strengthen accountability" of the Edinburgh parliament.
He will also back the devolution commission's previous recommendation to hand Holyrood control over Crown Estate responsibilities.
And in what is understood to be a reference to Department for Work and Pensions-run welfare-to-work schemes, he will call for devolution of "employment and skills policy".
He will also argue for Holyrood to be put in charge of its own elections.
However, the former transport and international development minister will also say further devolution should not undermine the Scots' "shared sense of belonging" or "social and economic rights" within the UK. He will insist on retaining UK-wide pensions, benefits and minimum wage, and ensuring resources can be shared around the country.
He will say: "After the referendum I believe that we must act swiftly to bring forward those proposals for change, working with other parties where needed.
"It would appeal to many Scots who want to see change, but without the risks, uncertainty and cost of walking away from the United Kingdom."
Mr Alexander, MP for Paisley and Renfrewshire South, will say Scots' appetite for leaving the UK has not increased as a result of the SNP's election victory in 2011.
And he will call them "a party of fainthearts" for demanding UK institutions such as sterling and the BBC in the face of the "granite-like resistance of the majority of Scottish people to separation".
Referring to the SNP's independence blueprint as "less a white paper and more of a white flag", he will joke: "I'm moved to ask the SNP - isn't it about time you stopped having the courage of our convictions and started having the courage of your own?"