This fourth anti money laundering directive (AMLD4) had already been approved by the European Council, the Parliament said in a statement.
The Directive requires countries to set up registers of the ultimate 'beneficial' owners of corporate and other legal entities including trusts.
The registers will be accessible by 'authorities' within each country, to 'obliged entities' such as banks doing due diligence into customers, and to people such as investigative journalists who can demonstrate a 'legitimate interest', the Parliament said.
The registers were not included in the European Commission's initial proposal, the Parliament said, but were added by MEPs during negotiations.
The text also sets out specific reporting obligations for banks, auditors, lawyers, real estate agents and casinos, among others, on suspicious transactions made by their clients, it said.
Rules on 'politically exposed persons' are also clarified in the text, the Parliament said.
Member states will have two years to transpose the AMLD4 into national laws.
MEPs also approved a 'transfer of funds' regulation, which aims to improve the traceability of payers and payees and their assets by setting out rules on information on the payer accompanying transfers of funds throughout the payment chain. This regulation will be directly applicable to all member states 20 days after publication in the EU official journal in June or July.
EU commissioner Věra Jourová welcomed the final adoption of the anti-money laundering package.
"Serious and organised crime is driven by profit - tracing the illicit proceeds of crime back to the criminal networks is essential both to detect, prosecute and dismantle those networks and to seize and confiscate their criminal wealth. The new anti-money laundering rules adopted today will help us follow the money and crack down on money laundering and terrorist financing," she said.
Money laundering describes the process where the proceeds of criminal activity are concealed by using the financial system to disguise the source of the money. Money laundering accounted for 2.7% of global gross domestic product (GDP) in 2009, or $1.6 trillion, according to the UN.
In February, when the rules were passed by two European Parliament committees, Judith Sargentini of the parliament's civil liberties committee described the vote as "a big step forward in the fight against tax evasion and a clear call for more transparency".
"With this vote Parliament has shown, from left to right, that it is in favour of public beneficial ownership registers … [T]he committees have shown that they are serious in their demand to finally break with the tradition of hidden company ownership," she said.
The Federation of European Accountants (FEE), which has been involved in developing the rules, welcomed the revised directive "and the high standards it promotes".
"Accountants and auditors across Europe play an important role in the fight against money laundering and terrorist-financing with their day-to-day work. FEE is committed to this fight, which is a shared responsibility for society as a whole," FEE said in a statement.
The UK has already confirmed that it will have publicly accessible company registers.