The Scottish Parliament should have the power to set income tax rates and bands, the body on strengthening devolution has concluded.
The Smith Commission also said a share of VAT should be assigned to the parliament, and Air Passenger Duty fully devolved.
The commission was set up by Prime Minister David Cameron in the wake of the vote against Scottish independence.
Its findings will form the basis of legislation on more Scottish powers.
The UK government welcomed the report, but Scottish ministers said it fell short of what the nation needed to flourish.
The Smith Commission, which took forward its recommendations in consultation with the Scottish Parliament's five parties - The SNP, Labour, Conservatives, Liberal Democrats and Greens - recommended that:
- The parliament should be given the power to set income tax rates and bands on earned income and will retain all of the income tax raised in Scotland.
- The parliament should be given powers to allow 16 and 17-year-olds to vote in Scottish elections.
- The parliament should be given powers to create new benefits in devolved areas and make discretionary payments in any area of welfare.
- A range of other benefits that support older people, carers, disabled people and those who are ill should also be fully devolved.
- The Scottish government and Scottish Parliament should have a "formal consultative role" in the process of reviewing the BBC Charter.
Scottish Secretary Alistair Carmichael said a "stakeholder group" would now be set up to take forward the recommendations.
The Liberal Democrat MP said: "Having a more powerful Scottish parliament inside a strong United Kingdom will open the door to more constitutional change in the United Kingdom.
"We can achieve home rule all round."
The Scottish government said any new powers were to be welcomed, but First Minister Nicola Sturgeon argued the Smith Commission package was ultimately disappointing because many powers, like the personal tax allowance, corporate taxation and child and working tax credits, would remain with Westminster.
Speaking at Holyrood, she said: "70% of our taxes continue to be set at Westminster, 85% of social security controlled at Westminster - this parliament responsible for less than half of the money we will spend.
"It's not so much the home rule that was promised - in so many respects, it's continued Westminster rule."
- Will the changes actually happen? BBC Scotland's business and economy editor, Douglas Fraser, tackles the question.
- The BBC's political editor Nick Robinson and deputy political editor James Landale have been looking at what the recommendations might mean for the rest of the UK.
- Lord Smith produced a 28-page report which was published on Thursday morning.
- Have a look at the main conclusions of the Smith Commission report.
- BBC Scotland political reporter Andrew Black explains the key issues and what the next steps are.
But shadow Scottish secretary Margaret Curran said the Smith report was, "a promise kept and an agreement delivered."
Speaking in Westminster, the Labour MP added: "Today's deal is, in fact, more radical and goes further than many had anticipated and on this side of the House we believe the principles we have worked for today - pushing power closer to people - is one that should be followed across Britain."
Mr Cameron said he was "delighted" with the report, adding: "We are keeping our promise to the Scottish people."
He added that proposals for English MPs to vote on English laws were to be published before Christmas.
Labour opposes the idea of only allowing English MPs to vote on matters that only affect England, claiming they would create two classes of MPs.
Instead, Labour wants more devolution within England. The Lib Dems also favour more regional devolution.
These new powers will deliver a stronger parliament, a more accountable parliament and a more autonomous parliament
Lord Smith, who chaired the commission, said: "Taken together, these new powers will deliver a stronger parliament, a more accountable parliament and a more autonomous Parliament."
"The recommendations, agreed between the parties, will result in the biggest transfer of powers to the parliament since its establishment."
Lord Smith's recommendations will form the basis of draft legislation due to be published by January 25, with the main parties at Westminster pledging to take it forward, regardless of who wins the UK election, in May 2015.
By Brian Taylor, BBC Scotland political editor
Detail, scrutiny, debate, discussion, bargaining, anger, leavening humour. But, as ever, the outcome is launched forth into the febrile soup that is the contest for public opinion.
The SNP strategy was to seek to maximise the gain from Smith - while simultaneously preparing to declare that the ultimate package is insufficient.
This is the tactical mirror of the approach adopted by the parties supporting the Union which is to argue that true Home Rule has been attained.
At Holyrood and in Scotland, the debate will be over whether the Smith report is a boon or a betrayal.
That will be a factor - a significant factor - in the Scottish facets of the UK General election in May.
By Nick Robinson, BBC political editor
If you think today's constitutional changes are only about Scotland, think again.
If you think they mark the end of a process of change, think again.
If you think they will end the debate about Scottish independence, think again.
The proposals to give the Scottish Parliament much more power will fuel calls for....
- More powers to be given to England's cities and regions as well as the Welsh & Northern Irish assemblies.
- Demands for English Votes for English Laws.
- Calls for even more powers for Scotland
- And different parts of the country to be able to experiment with different ways of doing things
By James Landale, BBC deputy political editor
There are calls - from all sides - for greater devolution within England. The Chancellor, George Osborne, is already offering more control to what he calls the "power houses" of the north of England such as Manchester and Liverpool.
In Wales, too, assembly members want greater control over their affairs and already Stephen Crabb, the Welsh Secretary, is holding cross-party talks to discuss what this might entail.
And in Northern Ireland, Stormont is expecting to be given very soon - perhaps even next week - the power to vary corporation tax so it can compete with the Irish Republic.
But there are risks.
Some MPs believe that these demands for extra devolution outside Scotland will not - and cannot - be met in full. They fear expectations will be raised that cannot not be satisfied and this will fuel resentment towards Scotland.
By Robert Peston, BBC economics editor
There are lots of other important new powers being transferred to Holyrood, including the ability to lower the voting age, change speed limits, license frackers, influence the new BBC Charter, and - possibly - change abortion rules.
But it is the transfer of big tax and spending powers that creates significant fiscal and economic uncertainties - whose resolution may have serious political consequences.
The lynchpin of all this is what the Commission calls the fiscal framework for the new devolution, which includes a number of principles.
Perhaps the most important is that at the precise moment that the new powers are devolved, Scotland's budget and the UK's budget should neither be bigger or smaller as a result of this transfer to Holyrood of new spending and taxing powers.