The former prime minister said the six changes he was proposing would transform the “unitary and centralised” system in the UK.
As part of that, he suggested that the Scottish Parliament should raise about 40% of the cash it spends and said giving Holyrood more powers over income tax was the best way to achieve this.
Mr Brown has submitted his proposals to Labour’s devolution commission, which will shortly put forward plans to boost devolution in the event of a No vote in September’s Scottish independence referendum.
In a speech in Glasgow, the former Labour leader said: “We need to build the future of the relationship between Scotland, England and the rest of the United Kingdom.
“I believe there are six constitutional changes we have got to make for a better relationship between Scotland and the rest of the United Kingdom, to turn what I would call a unitary and centralised state of the past into a partnership of equals and one where there is power-sharing across the United Kingdom.”
Mr Brown spoke out at the same time as former Liberal Democrat leader Sir Menzies Campbell said political parties should meet within 30 days of a No vote in the independence referendum to agree further powers for Scotland.
Sir Menzies said politicians should take advantage of the public appetite and momentum for more powers created by the independence referendum to act swiftly towards further devolution.
As part of his submission to Labour’s devolution commission, Mr Brown argued more tax-raising powers should come north.
Scotland is already due to get new powers over income tax from April 2016, when the UK Treasury will deduct 10p from standard and upper rates of income tax in Scotland and give MSPs the power to decide how to raise cash.
Mr Brown went further than this, though, saying: “The first 5p of income tax should be decided by the UK Government, the next 15p by the Scottish Government.
“I believe that is a fair way of raising 40% of the revenue of the Scottish Parliament in Scotland.”
This, he argued, would make Holyrood ministers “accountable to the people of Scotland for the way that money is spent”, adding: “They will have to answer at elections, which they don’t have to do at the moment, for tax decisions that they make.”
He also appeared to indicate the Scottish Parliament could get some power to alter the top rate of income tax, saying that “if the fairness of the Scottish Parliament was being undermined by unfairness elsewhere then there should be power to do something about it”.
The six key areas of Brown’s plan are:
• A new UK constitutional law - backed by an historic document equivalent to a bill of rights - to set out the purpose of the UK as pooling and sharing resources for the defence, security and well-being of the citizens of all four nations, including a commitment to alleviate unemployment and poverty.
• A constitutional guarantee of the permanence of the Scottish Parliament, backed up by a constitutional lock that prevents it being overruled or undermined.
• A new division of powers between Scotland and Westminster that gives Holyrood more powers in employment, health, transport and economic regeneration.
• A new tax sharing agreement that balances the commitment of the UK to pool and share its resources with the need for accountability to the electors in all the places where money is spent.
• New power-sharing partnerships to address shared problems on poverty, unemployment, housing need and the environment which, Mr Brown argues, cannot be addressed unless the Scottish and UK governments work together.
• A “radical” transfer of powers downwards from Westminster and Edinburgh to local communities.
Mr Brown’s plan is to be submitted to the Labour Party’s devolution commission and the party’s Scottish leader, Johann Lamont.
It would, he says, force Britain to change and lead to a revamp of the UK’s relationship with Scotland, and is “a far bigger, more modern, more forward looking - and ultimately more appealing - idea than that of a wholly separate state”.