The measure aims to boost Ukraine's economy by saving its manufacturers and exporters around €500m per year.
"The European parliament has supported an EU path for Ukraine for many years", said Pawel Zalewski, rapporteur on the 'reduction or elimination of customs duties on goods originating in Ukraine'.
"This is our first chance to demonstrate our support in practical terms, to help Ukraine during its current economic crisis in the face of dwindling currency reserves and increased pressure from the Kremlin", said the EPP deputy.
"The European parliament has always supported Ukraine on its European journey" - Pawel Zalewski
Speaking at a press conference before the vote on Thursday, Zalewski said, "As [Russian president Vladimir] Putin is closing Russian markets for Ukrainian exports, we are opening them".
"The European parliament has always supported Ukraine on its European journey" and this was the first vote to show real support for the Ukrainian economy which is facing a "deep economic and budgetary crisis", he said.
The Polish MEP hopes that these measures will "support" employment in the country and present the opportunity to "create jobs" in the future.
MEPs' backed the proposal by 531 votes to 88, with 20 abstentions.
While this EU trade preference does not require Ukraine to remove its own customs duties on imports from the EU, it does require Kyiv not to increase them for the duration the measure is in effect.
Imports from Ukraine must still comply with all EU rules on origin labelling and the legislation also entitles the re-imposition of tariffs if imports from Ukraine flood the EU market, causing, or threatening to cause, a serious disadvantage to EU producers of the same goods.
The Ukraine is a "major producer of coal", said Zalewski, stressing that an increase in the amount of Ukrainian coal on the EU market could threaten to "diminish Polish coal" production.
He said his proposal ensured this situation would be avoided as there remains in place a "possibility to suspend" the measure through the inclusion of a set of "safeguard clauses".
The measure now requires the approval of the European council, expected in April, before the proposal can take effect in May and would remain valid until 1 November 2014.