The European Parliament's Civil Liberties Committee voted 38 for and 19 against to approve the deal negotiated with the 28 member states last week, a statement said.
It now goes to the full parliament early next year, with approval expected in the aftermath of the attacks on bars, restaurants, the French national stadium and a concert hall which left 130 people dead.
Investigations have shown that several of those involved had travelled across Europe in the months before.
"We cannot wait any longer to put this system in place," said Timothy Kirkhope, the British conservative MEP who is steering the legislation through parliament.
"The choice is not between an EU PNR system and no EU PNR system; it is between an EU PNR system and 28 national PNR systems that will have vastly differing, or absent, standards for protecting passenger data," Kirkhope said in the statement.