Undocumented children will also be allowed to attend school in Sweden.
"I am very happy that we are able to solve this question together with the Green Party," said migration minister Tobias Billström to Swedish Radio News.
"This is the most important reform in ayslum policy since the temporary amnesty," said the Green Party's Maria Ferm who has negotiated the deal for her party.
"It is a big victory that this question can be solved, for all parents and children who are forced to live apart and for everyone who wants to preserve humanitarianism in Sweden," Maria Ferm told Swedish Radio.
850 million kronor (12.8 million dollars) has been set aside to implement the reform and enable families to be reunited.
DNA-testing could be one method used for those without documents. All the details are not complete and the reform will be put before parliament next spring.