The parliament largely followed EU President Donald Tusk's draft guidelines issued last week after British Prime Minister Theresa May formally triggered the historic Brexit process.
But they omitted any mention of the flashpoint issue of Gibraltar, unlike Tusk's guidelines which said that Spain should have the final say over whether any eventual trade deal applies to the British outcrop.
The Strasbourg-based parliament is the first EU institution to formalise its stance on the Brexit talks, passing the resolution by 516 votes for, 133 against and 50 abstentions.
The text insists that Britain must first make "substantial progress" on divorce terms -- the rights of three million EU citizens living in Britain, the exit bill and the fate of the border in Northern Ireland -- before striking a trade deal with the union.
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It says that MEPs are prepared to accept a transitional deal to ease the effect of Britain's exit from the EU's single market in 2019, but that it should be limited to three years.
Barnier said the message on phased negotiations should be that "the sooner we agree the principles of an orderly withdrawal, the sooner we can prepare our future relations in trade."
European Parliament President Antonio Tajani called for MEPs to be fully consulted on the negotiations, given that they must ratify the eventual agreement.
"I would like to recall that any possible final deal must be cleared by this house," he said.
The remaining 27 EU countries will rubberstamp Tusk's guidelines at a summit on April 29, paving the way for Barnier to begin formal negotiations with Britain at the end of May.
The resolution won the backing of all the major groups in the parliament, from the conservative European People's Party (EPP), the biggest bloc, to the Socialists and Democrats alliance, as well as the ALDE liberals, the Greens and the leftist parliamentary group GUE.
Parliament's Brexit negotiator Guy Verhofstadt said it was "key to have a united European Parliament together with the EU negotiator and the European Council," the forum for member states.