They backed a resolution tabled by the assembly’s Brexit steering group by 544 votes to 110 against.
Parliament also approved legislation enabling the transfer of the European Medicines Agency (EMA) from London to Amsterdam, due to Brexit.
MEPs pressed the European Commission and Dutch authorities to open the new facilities on time to “ensure a smooth transition” for the agency.
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The Brexit resolution approved in Strasbourg on Wednesday states that the future EU/UK relationship could be based on four pillars; trade and economic relations, internal security, cooperation in foreign policy and defence and thematic cooperation.
In a debate on the resolution, EU chief Brexit negotiator Michel Barnier said he was “quite comfortable with the framework the European Parliament proposes.”
Speaking later to reporters, European Council President Donald Tusk said “unfortunately Brexit was about disassociation not association. This is the first and most natural consequence of Brexit, the essence of Brexit.”
The resolution lays out a possible association agreement for future EU-UK relations after Brexit.
This relationship could be based on trade and economic relations (FTA), internal security, cooperation in foreign policy and defence and thematic cooperation, for example on cross-border research and innovation projects.
The resolution was drafted by the Brexit steering group, chaired by ALDE group leader Guy Verhofstadt.
It stresses the “uniqueness” of the EU system with its “binding common rules, common institutions and common supervisory, enforcement and adjudicatory mechanisms.”
The resolution now backed by Parliament says that any framework for the future relationship could not allow any sector-by-sector approach - cherry-picking EU laws. It should also preserve the EU’s “legal order,” including the role of the ECJ.
It also reiterates the importance of securing “equal and fair treatment” for EU citizens living in the UK and British citizens living in the EU.
The resolution sets out Parliament’s input ahead of next week’s summit in Brussels of EU heads of state or government, which is expected to approve the Council’s guidelines for negotiations on the UK’s future relationship with the EU.
Any withdrawal agreement and future association or international agreement with the UK will need to win the approval of the European Parliament.
Separately, speaking on Wednesday Irish Taoiseach Leo Varadkar said Brexit “is a threat to the Good Friday agreement” because it threatens to “drive a wedge between Britain and Ireland, between Northern Ireland and the Republic of Ireland, and potentially between the two communities in Northern Ireland.”
He argued, “I think for unionists - and I take no pleasure in this - it also creates risks for the union itself because it asks Scotland and Northern Ireland to leave the European Union even though the majority of people in both those countries voted not to do so.”