The bloc's assembly overwhelmingly backed the rules by 513 votes to 92 with three abstentions.
The package had already been agreed informally with EU member states who have joint say with the Parliament on the rules.
It marks the first set of EU rules to directly regulate the sector, which although widely considered not to have been a cause of the financial crisis, was still believed to be too opaque and lightly regulated.
Managers of all alternative investment funds, which also include real estate funds, must register to operate in the EU and report data to supervisors and meet capital requirements.
The EU assembly beefed up the draft proposals by including pay rules and restrictions on asset stripping on the private equity sector in a bid to stop them buying assets just for the short term.
The new regime dovetails with global efforts to shine a light on all parts of the financial markets - the United States has approved similar rules on registration and reporting but the EU rules go further.
The bulk of the EU's hedge fund and private equity sector is based in Britain which was locked in long negotiations with France who wanted a tough regime for non-EU managers.
(EurActiv with Reuters.)