The Community Charge Debt (Scotland) Bill has now completed its parliamentary hurdles.
The new law will effectively write off Â£425m of unpaid bills relating to the controversial household tax which was introduced by the 1989 Tory government.
The Scottish Conservatives were against the move but the Scottish government said it was the right thing to do.
The proposal to end the debt collection was brought forward last year by former first minister Alex Salmond after several councils said they would use the details of people who registered to vote in September's independence referendum to recover outstanding payments.
Deputy First Minister and Finance Secretary John Swinney said ahead of the final debate and vote: "The poll tax was a deeply unfair, regressive levy which should never have been introduced in the first place.
"A Tory government, which Scotland had rejected, imposed the tax on Scotland, and - as was recently confirmed in documents released under the 30-year rule - they were determined that Scotland be a guinea pig for their disastrous tax experiment.
"Although the poll tax is now defunct, its bitter legacy is still with us. It cannot be right that people fear being on the electoral registers because of decades-old debt relating to a discredited and unjust tax. Nor is it right that some of the few people paying off poll tax debt are the poorest in society."
Arrears collected by councils across Scotland fell to Â£327,000 in 2013-14 and some local authorities have already ceased recovery of the debt.
Councils are to receive a share of Â£869,000 from the Scottish government in 2015-16, based on what they could still reasonably expect to collect.
Gavin Brown MSP, finance spokesman for the Conservatives, said his party oppose writing off the debt, "not least because it sends completely the wrong message".
He added: "It could also encourage people who think they don't have to pay council tax because it will just be written off a few years down the line.
"We also think it's wrong that councils could be forced to lose out financially, when it's the Scottish government which has imposed this."
You can watch live coverage of the final debate at BBC Scotland's Democracy Live website from 3.45pm.
A new law to end the collection of historic poll tax debt has been backed by MSPs at Holyrood.