Bayo Ojo, the Nigerian justice minister and his Cameroonian counterpart, Maurice Kamto, signed the documents transferring sovereignty at a ceremony on Monday witnessed by UN, French and US officials.
The Nigerian flag was lowered at noon and that of Cameroon hoisted in its place.
Nigeria had agreed to withdraw its 3,000 troops from the peninsula in the Gulf of Guinea on Monday as part of a UN-brokered deal.
Yaounde had taken Abuja to the International Court of Justice at the Hague in 1994, which ruled in favour of Cameroon.
Nigeria rejected the ruling, saying that it did not take into account the interests of Nigerians living in Bakassi.
The United Nations intervened and the two countries set up a UN-chaired joint commission to solve the crisis.
"We yield ground in order to give way to peace. We give land in order to give room for life," Ojo said.
Ojo also sought to reassure Nigerian residents of Bakassi, many of whom have expressed concerns about living under Cameroonian rule.
The transfer, he said, "does not not mean an end in itself. You still have the opportunity of living here if you choose to do so".
Kieran Prendergast, the representative of the UN secretary-general, described the handover as "a good example of taking initiative in conflict prevention and solution", saying both sides were winners.