Launching a public consultation on the proposed tax, Mr Swinney said four out of five households would "be better or no worse off" under the new system.
He insisted that the proposals will mean the biggest tax cut in Scotland in a generation with those on low and middle incomes better off by an average£350 to£535 a year.
Under the proposals, on average
Single pensioners will be better off by £7.30 a week
Pensioner couples will be better off by £13.80 a week
Couples without children will be better off by £3.40 a week
Couples with children will be better off by £3.10 a week
One parent families will be better off by £5.40 a week
Single people will be better off by £3.30 a week
Households with multiple taxpayers will be better off by £2.50 a week
Only the top-income decile will, on average, pay more
Mr Swinney said: "Working with councils, we have already delivered a council tax freeze that will shelter vulnerable households from further increases - but the system is fundamentally wrong. Band D council tax has risen by 60% since 1997. It is time for a new approach.
"This new system will be the most significant improvement in local taxation this country has witnessed.
"The council tax is unfair, regressive and penalises people on low incomes. The people of Scotland will be better off paying a fairer, local income tax, based solely on the ability to pay. More than four out of five households will be better off or no worse off under our local income tax."
A spokesman for the Convention of Scottish Local Authorities said: "We're studying the detail in the consultation document and will respond in due course".
Removal of local tax-raising powers criticised
But Unison complained that the proposals would
Remove decisions and fund-raising powers from local government
The proposed level of the nationwide tax could leave a£900m hole in local government services
Allow the well-off to avoid paying for local services at all
Unison Scottish secretary Matt Smith said: “The government can’t have it both ways. They either set the tax at a rate which meets current local government spending - 6.5% according to the Burt review - or local services will be cut.
The 3% proposal falls "far short" of current spending. Even if money for council tax benefit is secured from the Treasury, the tax would have to be 4.5% to cover the hole, he said.
“Local government finance is facing its third reform in 20 years. This new tax on wages and jobs raises a huge number of questions and answers none. Politicians must face reality and deliver a solution that is fair and meets the costs of vital public services. This tax does neither.”