"We are determined to deploy the most robust force possible so that it can carry out effectively the difficult mandate the Security Council has entrusted to it," Adada said as the UN flag was hoisted.
"This means contributing countries deploy their personnel as quickly as possible."
The mission, the UN's largest, will eventually consist of 20,000 troops as well as 6,000 police officers and civilian personnel, but only around 9,000 troops and police are currently in place.
Additional soldiers from Egypt, Pakistan and Ethiopia as well as police from Nepal are to deploy in the next two months.
The force also needs a country to supply 24 helicopters to patrol an area the size of France.
Adada said that the mission's bid to bring lasting peace and stability to Darfur depended on "the active co-operation of the government of Sudan".
The Sudanese president has thrown up obstructions to the full deployment, including blocking Swedish and Thai troops from deploying.
Osman Yusuf Kibir, the governor of North Darfur and Khartoum's representative at the ceremony, stressed that his government was co-operating with the force.
"We are fully committed to implement what has been agreed upon with the United Nations and the government of Sudan and the African Union ... we stress our full co-operation and commitment to the agreement."
At least 200,000 people have died and more than two million displaced from their homes in Darfur since ethnic minority rebels took up arms against the Arab-dominated government in February 2003.
The underfunded and ill-equipped African force had struggled to bring peace to the region.
At least 50 African troops died during the mission, 12 in a single attack on a base in September that was widely blamed on one of the increasingly fragmented rebel groups.