The force of 1,500 guards would be able to deploy even if a member state did not ask for its help.
The European Commission said the force would work as a "safety net".
The proposal was approved a day after 4,500 people were rescued from boats in the Mediterranean near Italy.
National border guards in EU member states will be supported by the new European Border and Coast Guard in "exceptional situations", according to the European Commission.
The new force will "build" on Frontex, an existing EU agency that helps to coordinate national border forces, it said.
Plans for the new agency had faced criticism from some EU governments for allowing intervention even if member states did not request help in managing their borders.
Under the approved proposal, the EU Commission would propose an intervention and the European Council would make the decision.
"There should no longer be shortages of staff or equipment for operations at our external borders," First Vice President Frans Timmermans and Commissioner for Migration Dimitris Avramopoulos said in a statement.
"The external border of one Member State is the external border of all Member States."
The proposal will be sent to the European Council for final approval.
More than 231,000 migrants have arrived in Europe by sea this year, the UN says, compared to just over one million in total last year.
Monthly arrivals in April, May and June of this year were significantly lower than the same months in 2015.
A controversial deal between the EU and Turkey to tackle Europe's worst migration crisis since the Second World War came into effect in late March.
Several countries in the Balkans also sealed their borders amid the crisis, cutting off routes used by migrants to travel to northern European countries.
A note on terminology: The BBC uses the term migrant to refer to all people on the move who have yet to complete the legal process of claiming asylum. This group includes people fleeing war-torn countries such as Syria, who are likely to be granted refugee status, as well as people who are seeking jobs and better lives, who governments are likely to rule are economic migrants.
The European Parliament has approved a proposal to set up a new border and coast guard agency to help countries cope with unusually high levels of migration.