Petras Auštrevičius, parliament's rapporteur on the EU/Euratom/Moldova association agreement, said the decision was "a clear acknowledgment of the success of Moldova's political and economic reform process, which establishes its European prospects and bears witness to its determination eventually to join the EU".
MEPs backed the agreement by 535 votes to 94, with 44 abstentions.
"It is time to congratulate Moldova's people on this historic achievement, especially in the context of the upcoming parliamentary elections on 30 November, which will be crucial for the country", said the Lithuanian MEP.
"During my recent visit to Chisinau I signed a financing agreement for a new EU programme supporting [deep and comprehensive free trade area] implementation, for a total of €30m" - Johannes Hahn
Voicing his support for Auštrevičius's work on the dossier, European neighbourhood policy and enlargement negotiations commissioner Johannes Hahn also highlighted the importance of Moldova's upcoming elections.
"The EU stands ready to continue its close cooperation with a future democratically elected Moldovan government," he said, adding, "moreover, we are looking forward to a new impetus to the ambitious reform agenda after the elections."
"Corruption needs to be fought," stressed the Austrian official, saying, that Moldova's "justice and law enforcement systems need thorough modernisation and the business and investment climate needs to be improved. Only these key reforms will allow the country to unfold its full economic development potential.
"The EU will support Moldova in these endeavours," he said. "During my recent visit to Chisinau I signed a financing agreement for a new EU programme supporting [deep and comprehensive free trade] implementation, for a total of €30m, supporting small business, development of national legislation in line with EU quality standards and promotion of export and investment opportunities."
Reaction also came from chair of parliament's EPP group Manfred Weber, who said the vote, "brings Moldova yet another step closer to the European Union", adding that, "Visa-free travel to the EU has already been a reality since April this year."
"It is time to congratulate Moldova's people on this historic achievement, especially in the context of the upcoming parliamentary elections on 30 November, which will be crucial for the country" - Petras Auštrevičius
"Due to the determination of its government, the country has made significant progress in reforms and strengthening relations with the EU. This is necessary in order to put the country on the right track where people's aspirations for a free society, fair justice system and prospect for development should be at the basis of any political agenda.
"As I said in Chisinau this summer, in a situation where Russia closes its borders and creates economic problems, Europe opens its frontiers."
Weber's comments were echoed by EPP security and defence spokesperson Michael Gahler, who said, "The EU sees Moldova as a close partner. The association agreement brings Moldova substantially closer to the EU and comprehensively strengthens our relations.
"The EU offers a form of relationship that is based on negotiations, partnership, and solidarity, not on threats and violence. Our union is designed to ensure reconciliation and to make war impossible.
"The single market is our tool for innovation and the creation of jobs, wealth and social progress. This is what we have to offer Moldova."
"As I said in Chisinau this summer, in a situation where Russia closes its borders and creates economic problems, Europe opens its frontiers" - Manfred Weber
The deepening of EU-Moldovan relations was also welcomed by parliament's S&D group, with vice-president Tanja Fajon saying, "Moldova is making history being the first county of the eastern partnership to introduce a visa-free regime with the EU."
"It is extremely important that the benefits and advantages of the agreement are felt by the people. Once fully implemented it will provide better consumer protection and food safety, improved access to health services, more diverse and efficient use of energy resources and renewables and lower energy bills."
The Slovenian MEP also stressed that the agreement would "benefit the business sector with increased opportunities for small and medium enterprises" and "improve trade and create investment opportunities which will contribute to economic recovery and growth".
S&D vice-president for foreign affairs Knut Fleckenstein pointed to the geopolitical context under which the deal has been struck, with Russia's activities around the Ukraine crisis having a knock on effect on Moldova.
"Moldova is making history being the first county of the eastern partnership to introduce a visa-free regime with the EU" - Tanja Fajon
MEPs have been particularly critical of Russia's continued use of trade import bans on products from Moldova, with Moscow accused of attempting to destabilise the region.
Fleckenstein said, "This is not a move against any of the EU's or Moldova's neighbours and we can only regret that Russia perceives it as a potential threat.
"The association agreement, including the deep and comprehensive free-trade area, is a tool for further cooperation, peace and prosperity in our shared neighbourhood."
The deal is still awaiting approval from national parliaments, but was ratified by Chisinau in early July. Greens/EFA deputy Igor Šoltes will head up a delegation of seven MEPs to observe Moldova's parliamentary elections on 30 November.