Those transfers have taken place in some of the capital's most violent areas, including Haifa Street and the hard-line Sunni neighborhood of Adhamiya. Both areas are considered insurgent strongholds.
Today, there are some 4,000 Iraqis patrolling 10 Baghdad neighborhoods in place of U.S. forces. If the turnover is judged successful, a second wave of Iraqi soldiers is due to deploy into other neighborhoods in August.
According to Charles Heyman, a military expert with the Jane's Information Group in London, early reports suggest the Iraqi units are performing well. But he says weeks more will be needed to fully assess their capabilities.
"The very fact that they have been able to do [deploy in place of U.S. forces], to announce that, means there has been some progress forward," Heyman says. "But we need a little bit of time to actually work out what this actually means and what progress has really been made."
U.S. commanders say the Iraqi units are independently planning and carrying out their operations in the neighborhoods they control, and that U.S. forces provide additional support only when requested.
The patrols in the capital offer the Iraqi public a first daily chance to see the country's forces in action. Washington and Baghdad consider public confidence in the security forces as essential to isolating the insurgency, but until now the army has been seen mostly in training or in joint operations under U.S. command.
But the new patrols are only part of the effort to make the Iraqi army more visible.
Last week, Iraqi security forces launched what officials called their "first major" independent operation against insurgents northwest of the capital.
The Iraqi government initially claimed that commandos killed 85 insurgents on 24 March in a raid on what was termed the largest clandestine training camp to be discovered to date. However, much about the raid remains unclear. U.S. commanders have been unable to confirm the insurgent death toll, and some Iraqi officials have since downplayed the fighting as not "a major incident."
Heyman says the conflicting statements make it hard to judge how the now 2-year-old Iraqi army really did.
"Yes, there was a raid by Iraqi army commandos supported by [U.S.-led] coalition helicopters and other support agencies," Heyman says. "And it was relatively successful; it probably unbalanced the insurgents. But it was not quite as successful as the Iraqi government would like us to believe at the moment."
Still, analysts say that even only a "relatively successful" operation contrasts markedly with the performance of the Iraqi army a year ago.
Many of the first soldiers trained by the U.S. deserted or refused to fight alongside U.S. Marines trying to re-establish control over Al-Fallujah in April. Others refused to fight against insurgents in Baghdad's Shi'a neighborhood of Al-Sadr City.
Since then, some soldiers have been dismissed, others hired, and training has intensified. The Iraqi government has also partially reversed an earlier U.S. decision to exclude former top officers of Saddam Hussein's regime from joining the new army.
Heyman says the Iraqi army's biggest challenge for the future is to develop a leadership that the soldiers trust and will follow into battle. He says bringing back trusted former officers is part of that process, as is developing new leaders within the ranks.
"One of the things [about any army's] high command and the top leadership is that soldiers have to trust people," he says. "And trust comes after a number of factors. But one of them, of course, is confidence in the ability of that leader based on his actions in the past. And that is one of the reasons you have to bring in some of the more trusted members of the Saddam-era army, because there were some very, very good officers in that army -- people who managed to hold things together when a lot was falling apart around them."
One notable returning officer is Jawad al-Dainiy, who joined in November. He is a 57-year-old general who received some 24 medals from Saddam Hussein over the course of a 30-year military career. He now leads a brigade due to grow to 5,000 soldiers.
Today, the Iraqi Army is reported to number some 50,000 soldiers. But the actual number of soldiers in the Iraqi army and other security forces who are now combat ready is uncertain.
U.S. Secretary of the U.S. Army Francis Harvey told reporters in Washington on 23 March that there are 145,000 Iraqi security personnel, including army and police.
But official counts have varied widely in the past. A year ago, the U.S. Defense Department put the total number for police and military personnel at 206,000, then later revised it to 132,000, and finally to 90,000 by September.
The U.S. daily "The Christian Science Monitor" reported this week that high official numbers have previously included substantial numbers of people who guard facilities -- essentially night watchmen -- and administrative personnel.
The Iraqi government says it wants 100,000 fully trained soldiers by midyear and 150,000 by the end of the year. However, U.S. commanders have declined to say whether they are on track to meet those goals.