After months of deadlock, the parliament also passed an annual budget and a law that paves the way for the granting of amnesty to thousands of political detainees.
De Mistura hailed the passing of "three important laws".
"This is exactly what we hope to see in terms of democracy," he said.
"It is made of compromise, it is made of debate but it is also made of results."
Meanwhile, Iran has postponed a scheduled round of talks with the US on Iraqi security in Baghdad, giving no reason for the delay.
Hoshiyar Zebari, the Iraqi foreign minister, said the talks were to have been held on Friday.
Zebari said: "Yesterday we were informed that the Iranians want to postpone this for some time, for some unknown reason."
"This is the fourth time that we agreed on a date and they don't show up."
US and Iranian officials met three times last year in Baghdad to discuss security in Iraq in talks arranged by the Iraqi government.
Manouchehr Mottaki, the Iranian foreign minister, said that the next round of discussions would take place at an expert level.
He was referring to a security committee made up of officials from both sides.
Washington accusses Iran of supplying weapons and training to Shia militias in Iraq.
Tehran denies the accusations.