Sweden's Chancellor of Justice Göran Lambertz agreed to the sum after consulting with Alzery's lawyers, Nyhetskanalen.se reports.
"He wanted a bit more but now they have agreed to this settlement. It is based on the suffering he endured during his deportation from Sweden and the torture he was exposed to in Egypt," Lambertz told news agency TT.
The Chancellor of Justice added that there was good reason to believe Alzery was telling the truth when he said he was tortured on his return to Egypt.
When asked whether three million kronor was a reasonable sum, Lambertz said it was "maybe a bit high."
"But it was important to reach an agreement with him and his lawyer and in that respect we thought it was a reasonable amount to pay," he said.
Mohammed Alzery and Ahmed Agiza 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.
The Swedish government sent them back to Egypt despite having insufficient diplomatic guarantees that they would not be tortured upon his arrival, something for which Sweden has faced criticism, including from the UN Torture Committee.