Reunification has been hampered since spring 2010 when Sweden tightened its family immigration law, taking stringent measures toward those that did not have recognized identity documents.
Thousands of Somalis have thus been stranded in crowded refugee camps in east Africa during the current famine.
Changes in the law mean that about 4,000 Somalis, many children, will be permitted into Sweden though it is not certain if all will receive a residence permit.
In addition, the new agreement grants undocumented children the right to attend school, a promise made by Sweden's Minister for Education Jan Björklund.
The budget for autumn 2012 allocates 850 million kronor (about $130 million) toward the cost of the legislative reforms and the undocumented children's education. However, the exact cost and total number of those covered remains unclear, according the Dagens Nyheter (DN).
The newfound cooperation between the Alliance Parties and the MP stems from the new labour law, a law that answers Sweden's need for a future workforce by opening the door to those who do meet the stringent requirements of the asylum law.
The proposed bill regarding the reunification and education of undocumented children will be presented later this year.