The former Prime Minister yesterday urged Labour colleagues to adopt detailed proposals to increase the amount of tax revenue levied by Holyrood.
In a 20-page submission to the party's devolution commission - which is due to present its policy recommendations later this month - he said the Scottish Parliament should set a bigger share of income tax and suggested MSPs should have complete control over the top rate.
Under the 2012 Scotland Act, Westminster will set income tax rates 10p lower in Scotland than the rest of the UK and leave MSPs to approve a "Scottish Rate of Income Tax" (SRIT) across the basic (20p), higher (40p) and additional (45p) bands.
They will be able to make up the shortfall exactly or raise or cut income tax compared with the rest of the UK.
Unveiling his plans at an event in the East End of Glasgow, Mr Brown said the portion set by the UK should fall to 5p, requiring Holyrood to set a 15p rate to match UK levels.
He also suggested the additional rate - which Labour shadow chancellor Ed Balls has pledged to raise back to 50p - should be devolved to Holyrood to prevent fairness being "undermined". He said the split was a "fair way" of taking the revenue raised by Holyrood to 40% of the money it spent.
The move, he said, would make ministers more accountable, adding: "They will have to answer at elections, which they don't have to do at the moment, for tax decisions that they make."
Mr Brown described the deal as "maximum accountability" without eroding the UK's ability to pool resources for what he called "covenanted" rights, including common pension and welfare entitlements.
He ruled out devolving corporation tax, warning it would lead to a "race to the bottom" as authorities competed with each other to lower rates.
VAT could not be devolved under EU rules, he said, while National Insurance should remain UK-wide because of its link with pensions.
The measures were part of a six point plan to create a "partnership of equals" within the UK.
He also called for a Bill of Rights-style law explaining the purpose of the UK as pooling and sharing resources for the defence, security and well-being of people in all four nations.
Other plans included making Holyrood permanent legally, handing the parliament a range of new powers in fields such as transport and work programmes, extra powers for local councils and "power-sharing partnerships" to ensure different administrations worked together.
The proposals comes as Scottish Labour's devolution commission, made up of senior MPs, MSPs and party members, prepares to present its recommendations.
The party has been split over the extent to which further tax powers should be transferred to the Scottish Parliament but sources last night said Mr Brown's vision hinted at the "direction of travel" Labour was taking.
His tax proposals are significantly less radical than plans outlined in a interim report by the devolution commission a year ago.
Last April the group said there was a "strong case for devolving income tax in full".
Addressing supporters, community leaders and trade unionists Mr Brown said: "We need to build the future of the relationship between Scotland, England and the rest of the United Kingdom."
John Mason, SNP MSP for Glasgow Shettleston, added: "Mr Brown had three years as Prime Minister - he could have implemented all these ideas then, but didn't.
"The closer we get to the referendum, the clearer it becomes that the only way to ensure Scotland gains the powers we need to make decisions in areas such as tax and welfare is with a Yes vote."