Donald Tusk says he and his cabinet will be sworn in next week.
Warsaw had previously been one of most vocal supporters of the US policy in Iraq.
Polish troops took part in the invasion in 2003, sparking a bitter verbal confrontation with anti-war European Union members, notably France.
US-Polish ties strengthened after the election in 2005 of the previous Law and Justice party administration.
The conservative government of prime minister Kaczynski, the identical twin of the current Polish president, Lech Kaczynski, had said it was planning to send a new group of soldiers in 2008.
Tusk’s Civic Platform, which won October’s snap general elections, had earlier pledged a swift pull-out of Polish armed forces from Iraq.
Tusk said in November it was important that Washington recognise that his Civic Platform had won power with a pledge to “end the mission in Iraq at least in its current form, in 2008”.
In October, Edward Pietrzyk, Poland’s ambassador to Iraq, was seriously injured and his driver killed by a roadside bomb in Baghdad.
A total of 22 Polish soldiers have been killed in Iraq since 2003.
The current 900-strong Polish contingent is stationed in the Diwaniyah region of Iraq, where 2,600 were deployed in 2003.
A public opinion poll last June found that 81 per cent of Poles were opposed to their soldiers’ deployment alongside US troops in Iraq, with only 15 per cent in favour.