General Dunford, who earned the nickname "Fighting Joe" for his leadership in Iraq, took command of the International Security Assistance Force (ISAF) on Sunday in a ceremony at the group's headquarters in Kabul amid tight security.
"Today is not about change, it's about continuity. What has not changed is the will of this coalition," he told a crowd of foreign and Afghan officials.
Afghan president Hamid Karzai was absent from the change of command ceremony despite receiving an invitation from ISAF. A spokesman for Mr Karzai declined to comment on his reason for not attending.
General Allen was the fourth ISAF commander under US president Barack Obama, and his 19-month tenure was punctuated by a series of crises, from the accidental burning of Korans at a US base to images of US soldiers urinating on the bodies of Taliban fighters.
There has been also been a surge in so-called "green on blue" insider attacks, in which Afghan security forces turn their weapons on their NATO allies.
The outgoing commander said victory over the insurgency led by the Taliban would "never be marked by a date, a point in time in the calendar" but insisted the effort would prevail.
"The insurgency will be defeated over time by legitimate and well-trained Afghan forces," General Allen said.
"Afghan forces defending Afghan people and enabling the government of this country to serve its citizens - this is victory, this is what winning looks like."
There was also controversy about General Allen's own conduct after he became embroiled in the sex scandal that brought down David Petraeus, the CIA director and his predecessor as ISAF chief.
The Pentagon exonerated General Allen last month over emails he sent to a woman tied to the Petraeus affair, which defence officials had said were potentially "inappropriate".
The White House said last month it would nominate General Allen as NATO's supreme allied commander in Europe.