The first moves started at dawn on Sunday, and the troops say they met very little opposition when beginning to take control.
Captain Roger McMillan of the Royal Scots Dragoon Guards said: "We have pushed on the door of Basra and it opened. We are going to be staying."
At Iraq's capital city Baghdad, US military bosses say they are close to controlling every road into the city.
Days after they first took control of the international airport in Baghdad, the first US military aircraft has landed there.