On a visit to Iraq, he said 2008 had been a "critical year" for re-establishing security there.
The fact recent provincial elections had passed without incident had given a "new momentum", he added.
UK military operations in Basra are due to end by 31 May. Most US troops are expected to withdraw by August 2010.
US President Barack Obama is due to announce the withdrawal plans later although it is expected that up to 50,000 will remain in Iraq.
Mr Miliband told BBC Radio 4's Today programme politics in Iraq were now moving "onto a more normal basis" and the government could start concentrating on the economy and public services.
Having spoken to Iraqi PM Nouri al-Maliki and other Iraqi leaders, Mr Miliband said he believed gains made in Iraq were now "more sustainable".
"Every week that goes by I think strengthens Iraqi capacity and every week that goes by strengthens the confidence of the Iraqi people," he said.
On Thursday Mr Miliband announced a £277m ($400m) joint venture involving a UK-based petroleum company drilling for oil in Iraq.
He said it sent a message to British firms Iraq was "open for business".
He said Iraq was rebuilding itself after years of suffering.
But he said the US had "enduring commitment" to improving local security forces after most troops leave.
"I think the Iraqis on the one hand are impatient to run their own affairs, on the other hand they recognise the vital and massive nature of the American contribution, and the help that it can give to them," he told the BBC.
"I think there is a real yearning here for Iraqis to run their own affairs, to make their own mistakes but also to make their own progress.
"What the Iraqis now need to focus on are issues like economics and the electricity supply which are the bread and butter of politics around the world."
UK forces have lost 179 troops since the 2003 invasion and have a 4,100-strong force in the country.
President Obama is due to announce later his plan to withdraw most US troops from Iraq by August 2010.
He is expected to say troop numbers will be reduced from the current 142,000 to about 50,000.