The contingent of 1,400 Ugandans is due to replace Ethiopian soldiers, who were invited by the transitional Somalian Government to try to suppress the clan militias and Islamic forces opposing it.
The AU troops have been stranded at Mogadishu airport through six weeks of some of the fiercest fighting seen in the capital in 15 years.
At least 1,300 people were killed and thousands more have fled the city.
AU commander General Edward Wamala says there is a degree of security now in Mogadishu but it is too early to talk of peace.
"It may be too early to have a full celebration of what has been achieved before we do a full mop-up of the remnants of the guys who have been causing trouble in Mogadishu's town," he said.
"So I think if that's not yet done, there could be sporadic instances of insecurity, which could happen off and on in some parts of the city."
More troops pledged from other African countries have yet to deploy.
The United Nations Security Council on Monday ordered the world body to draw up contingency plans to deploy UN peacekeepers to take over from the AU force, a prospect many view as unlikely unless Somalia becomes more stable.
The presence of soldiers from Ethiopia, the traditional rival of Somalia, has inflamed some of the clashes and given insurgents fighting the Government a rallying cry among the usually nationalistic Somalian.
The Government on Saturday declared victory and began sweeping insurgency strongholds for weapons, fighters and looters, but many are sceptical that the insurgency is over.
Islamist leaders in exile in Eritrea have said their fighters have just fallen back to regroup and change their tactics.
The United Nations has warned of a looming catastrophe, with 365,000 people fleeing Mogadishu since February, most of them clinging to survival in nearby towns or out in the open.
- Australian Broadcasting Corporation
- © ABC