Agiza, who remains imprisoned in an Egyptian jail, had demanded 35 million kronor from the Swedish state.
His legal representative Anna Wigenmark said her client had accepted the Chancellor of Justice's offer with a degree of hesitancy.
"He is primarily dissatisfied with the difficult situation in which he currently finds himself. He feels that he has been treated unfairly. He is not doing at all well. He has suffered serious mental and physical damage," she told the TT news agency.
Ahmed Agiza and Mohammed Alzery were expelled from the country following a deportation order by the Swedish government. They were handed over to US agents at Bromma Airport in Stockholm and were flown to Egypt on an American government plane.
In July this year, Mohammed Alzery was also awarded three million kronor by Sweden's Chancellor of Justice Göran Lambertz, who agreed to the sum after consulting with Alzery's lawyers
The Swedish government sent both men back to Egypt on December 18th 2001 despite having insufficient diplomatic guarantees that they would not be tortured upon arrival, something for which Sweden has faced criticism from organizations including the UN Torture Committee.
The men had their hands and feet cuffed and hoods placed over their heads immediately prior to the deportation. Swedish Security Service Säpo had suspected them since May 2001 of links to a terrorist organization.
Once back on Egyptian soil, Agiza was sentenced by a military court to 25 years in prison, a sentence that was later reduced to 15 years.
Alzery was held without charge in an Egyptian prison until October 2003. Both men claim to have been tortured while in prison.