The inquiry will likely examine the circumstances leading up to Britain's decision under Brown's predecessor Tony Blair to join the US-led invasion in March 2003, and its aftermath.
The government now faces controversy over whether or not the probe will be held in private, as Miliband has indicated.
Opposition politicians and relatives of British soldiers killed in Iraq are urging full transparency.
"If he (Prime Minister Gordon Brown) holds it all or partly in secret and kicks the eventual report into the long grass, it will be a betrayal of all those families who lost children serving in Iraq," Clegg told the Observer.