The official Petra news agency said on Sunday 58 of the 98 lower house deputies present voted for the law on the National Centre for Human Rights (NCHR).
An initial vote set for Wednesday was postponed after a row broke out in the 110-seat lower house over a clause stating that the centre should not deal with "the Jewish entity and those who support it".
But Sunday's vote removed the wording from the law, Petra said.
Several Islamist MPs had wanted the clause kept in but deputies opposed to it, including conservatives, argued that it would portray Jordan, which has a 1994 peace treaty with Israel, as a "racist" country.
The NCHR was first set up more than a year ago by royal decree and functioned under the chairmanship of former prime minister Ahmad Obeidat.
Its membership comprises a number of human rights activists and former senior officials.
The goals of the centre are to promote human rights, ensure equality and justice, fight discrimination, enhance democracy and to observe the kingdom's commitment to international conventions.
Jordan signed a peace deal with
Israel in 1994
According to the pro-government daily Jordan Times, "the NCHR has the right to contact other concerned organisations in the world to exchange experiences and print publications".
"The NCHR, according to the law, will have full independence which means that its offices cannot be searched by security bodies without written permission from court. Moreover, the centre will be independent financially and administratively."
Jordan's human rights commissioner, Walid Saidi, said last
week that the centre did not have any ties with Israel but at the same time was open to all religions.
The Middle Eastern country has been much criticised for its human rights record.
Rights group Amnesty International said in a recent report that dozens of political prisoners were arrested in the past year.
The report said political trials continued whose procedures failed to meet international fair trial standards, and there were reports of torture and ill-treatment of detainees.
Moreover, Amnesty said restrictions continued to be imposed on the right to freedom of expression and on the press.