Italian authorities have been investigating Amazon for tax evasion in the period between 2011 and 2015, but the deal meant the case is now closed, it said in a statement.
Citing investigators, Italian media reported in April that Amazon had established a mechanism to declare some €130 million of Italian profits in Luxembourg, which has a much lower corporate tax rate.
Italy has previously forced other US internet giants to pay up for taxes owed, including Apple, which in December 2015 agreed to pay €300 million to end a tax fraud investigation. Last May, Google agreed to pay €306 million.
The tax authorities said on Friday that they would now seek "preventative agreements" with Amazon to ensure that the company properly pays its taxes on Italian earnings.
It also "confirmed its commitment to a policy of fiscal control concerning Italian operations of internet multinationals".
Amazon said the deal concerned "historical matters" and that it created an Italian country branch in 2015 "with all retail revenues, expenses, profits and taxes due now accounted for in Italy".
In a statement, Amazon also said that it had invested more than $800 million in Italy since 2010 "and created over 3,000 jobs".
US web giants are regularly accused of trying to wiggle out of their tax obligations, often by choosing lower-tax countries for their headquarters.
The European head office of Google is located in Ireland, where corporate tax rates are amongst the continent's lowest.