But the decision to hold the inquiry in secret has come under public criticism.
"I think many people will be disappointed, it is another secret inquiry," Lindsey German, from the Stop the War Coalition, which protested against the Iraq war, told Al Jazeera.
"It's carried out by the privy council, which is part of the establishment and therefore won't be genuinely independent of the government. There is no reason this shouldn't be a public inquiry."
In an interview with Britain's Observer newspaper on Sunday, Nick Clegg, the leader of the Liberal Democrats, the country's second-largest opposition party, also warned of the dangers of holding the inquiry in secret.
Clegg was quoted as saying: "If he [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.
"They need answers, not another Whitehall stitch-up."
The investigation will examine the circumstances leading up to Britain's decision under Tony Blair, Brown's predecessor, to join the invasion, and its aftermath.
David Miliband, the UK's foreign secretary, had said in March that a probe would be held soon after almost all of Britain's 4,100 troops withdrew from Iraq by the agreed date of July 31.
Rose Gentle, an anti-war campaigner whose soldier son Gordon died while serving in Iraq, said: "We already feel that we've been lied to by the government. We don't want any more lies."
The announcement comes as Brown strives to reassert his badly damaged authority over his own party.
A scandal over politicians' expenses and historically bad results in European and local elections have prompted a wave of ministerial resignations and calls for him to resign.
A total of 179 British military personnel have died since March 2003 while serving in Iraq.