British forces will hand back control of security in Basra province to Iraq on Sunday, it has been confirmed.
Mr Brown had said the handover would take place within two weeks
An Iraqi government spokesman announced that "the handover would go ahead on the 16th of this month".
The UK's Maj Mike Shearer said the setting of a date for the handover to Iraqi authorities was a "very positive step in the right direction".
Gordon Brown said the move would take place inside two weeks when he visited British troops in Iraq at the weekend.
Maj Shearer told BBC Radio 4's The World at One: "We absolutely welcome the announcement that we are going to move to Iraqi provincial control on the 16th.
"That's a very positive step in the right direction and clear recognition that the security situation is such that the Iraqi security forces are able to take on that responsibility."
The prime minister said the province - the final area of Iraq which is still under UK control - would be handed back when he addressed troops at Basra air station on an unannounced visit.
Mr Brown's announcement followed telephone talks with Iraqi Prime Minister Nouri Maliki.
Ministers announced in October that December would be the deadline for the handover.
The 4,500 British troops still in Iraq will now focus on training Iraqi forces. UK troop numbers are set to be reduced to 2,500 from the spring.
Maj Shearer said: "I am absolutely confident...that the Iraqi security forces here in Basra are ready to take on responsibility for policing their own streets."
The Iraqi announcement came as three car bombs exploded in the southern city of Amara, in neighbouring Maysan province, which police say killed at least 39 people and injured more than 100.
In the Commons, acting Liberal Democrat leader Vincent Cable said the "continuing tragedy" in Iraq was the "real disaster" for the prime minister.
Mr Brown said Iraq now had a democratic government and that violence was down 90% in recent months.