Labour's National Policy Forum (NPF) has agreed a binding commitment to include a new Scotland Act in the party's first programme of government if it wins the 2015 general election.
Its proposals for more powers to be transferred north - including giving Holyrood more power over income tax and responsibility for housing benefit - will be included in the party's election manifesto.
Ms Curran said: "More powers for the Scottish Parliament are guaranteed next year. This decision today means that Labour's commitment to pass powers over tax, jobs and welfare to the Parliament will be included in our manifesto for the 2015 election and a new Scotland Act will be in Labour's first Queen's Speech.
"And I want to give a personal guarantee that if I am Secretary of State for Scotland next year, getting this legislation through Parliament will be my top priority from day one of the next Labour government."
Labour's NPF also backed Labour's platform for the general election, which includes plans for an energy price freeze, a jobs guarantee for young people funded by a tax on bankers' bonuses and powers to enable public sector operators to compete for all rail franchises
Ms Curran said: "Today, we set out our plans for the next Labour government. It is a radical and bold programme. From the energy price freeze, to the jobs guarantee for our young people, to getting a better deal for our railways, this is a plan that will change our country for the better, and help thousands of families across Scotland.
"The best way to deliver progressive policies is by working together with our friends and allies across the UK. Not by splitting apart. That's why people should vote no in September, but say yes to changing Britain with Labour next May."
But SNP MSP Joan McAlpine said Labour's Devolution Commission, the group that drew up the proposals, is "as weak as water and fools nobody".
She added: "The Scottish Social Attitudes survey shows that 63% of people in Scotland want full powers over tax and welfare - what Labour is talking about is light years from this, and it isn't something the Westminster system has ever shown any interest in delivering. Only independence delivers these vital powers.
"The only way to complete the powers of the Scottish Parliament, and create the fairer society and more prosperous economy we all want to see, is with a Yes vote for an independent Scotland in September."