Two parliamentary groups, the Socialists and the Liberals, said on Thursday they would back the agreement, after vetoing a previous version in February due to concerns about insufficient privacy safeguards.
The Parliament's dominant centre-right European People's Party (EPP) group also backs the agreement.
Under the agreement, struck between the US Treasury, EU member states and the European Parliament, so-called "scrutineers" appointed by the European Union will become part of the US Treasury's operations that examine the financial transactions of terror suspects, MEPs said.
A US Treasury Official was reported to have met with the Commission on Wednesday to agree on the details, but did not meet with parliamentarians.
The socialist (Socialists & Democrats) and EPP groups in the European Parliament claim they have managed to open up negotiations that were deemed shut by EU Home Affairs Commissioner Cecilia Malmström last week.
"We have a highly desirable deal for European citizens," said Claude Moraes, a socialist member of the European Parliament from the UK.
Caving in?
The agreement has been heralded as a great win by the S&D and EPP camps, but the Greens have accused the two groups of caving into an agreement they still view as unacceptable.
The Greens say yesterday's agreement damages the EU's negotiating position with the US on data protection, a review of which is due to begin in the autumn.
Their complaint stems from bulk data transfers, which would still be possible once the agreement is back on its feet.
Ideally, the Parliament would want to replace bulk data with targeted searches carried out by an EU-based authority to prevent Treasury officials from poring over swathes of citizens' private data.
"We cannot reduce the problem of bulk data for the moment as we do not have the technical capability," Birgit Sippel, a German S&D MEP, told EurActiv.
As part of the agreement, the European Commission has been asked to write a framework for the extraction of data on US soil with a view to setting up an EU equivalent to the American Terrorist Finance Tracking Programme.
If after five years an EU equivalent is not in place, the Commission will either have to renegotiate or terminate the agreement, German liberal MEP Alexander Alvaro told EurActiv.
A spokesperson from the US Mission to the EU was unavailable for comment.
