It proposed that the UK Treasury should deduct 10p from standard and upper rates of income tax in Scotland and give MSPs the power to decide how to raise cash.
The new powers would be combined with a cut in the block grant, currently about £32bn, which Scotland gets from the UK Government.
The report also said MSPs should gain control over stamp duty, landfill tax and air passenger duty, as part of proposals which would see Scotland controlling more than a third of its budget.
The commission, chaired by Sir Kenneth Calman, also said powers to run Scottish elections should be handed from Westminster to Holyrood.
Devolving nature conservation at sea to Scotland was also among its 24 recommendations.
Sir Kenneth, a former chief medical officer for Scotland, concluded devolution had been a "real success" after 10 years, but could work better.
"Our radical and innovative proposals to introduce a new Scottish rate of income tax will significantly strengthen the accountability of the Scottish Parliament and enable it to serve the people of Scotland better, with a union secure for the future," he stated.
Sir Kenneth Calman said Holyrood should be less dependent on Westminster for funding
The commission also put forward reforms to make Holyrood and Westminster work better together, including "state of Scotland" debates at the UK parliament.
The body was voted in at Holyrood in 2007 by Scotland's main opposition parties - Labour, the Liberal Democrats and the Conservatives - and was supported by UK ministers.
The Scottish Government criticised the commission, because it was not looking at the issue of independence and ruled out Westminster handing full financial powers to Scotland.
SNP ministers have their own rival constitutional review - the National Conversation - currently under way.
The Calman steering group will consist of the Scottish Labour, Tory and Liberal Democrat leaders, as well as Scottish Secretary Jim Murphy - who said talks would be taking place with the Treasury on how the proposals could be implemented.
Scottish Labour leader Iain Gray welcomed the report as an exciting development in devolution.
He added: "It is bold and progressive. Ten years on, the Calman Commission has rigorously examined how we can make the Scottish Parliament more accountable."
Tavish Scott, the Scottish Lib Dem leader, said: "Calman's recommendations take us towards a real home rule settlement. Politicians should not be able to take easy spending decisions without the responsibility of accounting for this money."
His Scottish Conservative counterpart, Annabel Goldie, said: "This is a hugely significant and thorough piece of work. It is our duty to cement Scotland's place in the Union and to strengthen devolution."
Scottish Secretary Jim Murphy described the report as "a promising and well-evidenced basis on which we can work".
He added: "The suggested changes are of course complex and require detailed and careful consideration but along with the Treasury we will assess and explore how to implement these proposals."
The Scottish Government's constitution minister, Mike Russell, said he would welcome any extra powers for Scotland.
But he added: "Full fiscal autonomy has the great benefit of allowing the Scottish Parliament to make its decisions based on a range of taxation - not just income tax, which is a very blunt instrument."
"At present, we have a pocket-money parliament - under the Calman proposals, Scotland would have a Saturday job but the pay would be deducted from our pocket money."
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