It would allow parties to compete in elections based on political platforms.
The previous system encouraged formation of dozens of small parties and voting for tribal affiliation. That produced docile legislatures dominated by conservative backers of King Abdullah II.
Up to now Jordanians have been hesitant to join policy-based political parties for fear of retribution from the state.
The new law declares that the government will "respect the constitutional right of citizens to political affiliation."
It also allows for financial assistance from the government, but it prohibits foreign aid to the parties, so that their allegiance will remain to Jordan.
Most restrictions in the previous law, such as allowing the government to monitor activities and financial records of political parties, have been revoked.
In their debate Wednesday, lawmakers described the new law as "progressive."
Islamist opposition member Abdul-Latif Arabiyat said the law is a "step forward." He represents the Islamic Action Front, the political arm of the Muslim Brotherhood, Jordan's largest opposition group.
He said another reform measure, redrawing districts that now favor the king's backers, must be next. Critics have charged the current map maximizes representation for Bedouin tribes, which traditionally support the monarchy.
"What's important is the electoral law, which we are eagerly awaiting," Arabiyat said.
There have been 17 months of relatively mild street protests calling for curtailing some of the king's absolute powers.
Abdullah is trying to satisfy activists by giving elected representatives a greater say in politics. He promised to allow the elected parliament to choose a prime minister, but he did not say when.
Under the current system, Abdullah has the sole power to appoint all Cabinet members.
Parliamentary elections are expected later this year.
Last year, Jordan changed 42 articles in its 60-year-old constitution, giving parliament a stronger role in decision-making.
Also, an independent local election commission was set up to supervise the next round of elections. The king said he wants a constitutional court to monitor the implementation of amended laws.
Under the present system, Jordan has 33 fragmented political parties. The government wants to merge them into several core coalitions.
Officials have floated the concept that Jordan could eventually have two or three main parties, and the party winning a majority of seats in parliament would form a Cabinet.