The toi moko and koiwi tangata will be taken to Te Papa in Wellington, where a ceremonial welcome will be held by local iwi.
The museum will care for and house the remains in a guardianship role until their origin can be established.
Te Papa's kaihautu, Arapata Hakiwai, thanked the university for its proactive engagement.
"We are so pleased to be here today to be able to take our ancestors home. We will continue our work in New Zealand to establish which part of our country they originate from."
June Jones, the religious and cultural leader of Birmingham University's Medical and Dental Sciences College, said the university had no records about how the remains came to be in storage at the university.
"But when they were uncovered, we knew we had to give them back. We believe that to keep them would be wrong. They belong back with their own people, to be treated with the dignity and respect they deserve."
Dr Jones said the university had been working with Te Papa on the repatriation of the remains for nearly three years.
"I am so pleased to be able to hand them back to the people who will take them to where they belong. It was a huge honour to welcome Maori elders and members of the museum repatriation team to the University of Birmingham."
Dr Jones said the university would continue to work with Te Papa to help identify other medical schools and institutions in the UK which may have Maori human remains.
"Whilst there are controversies surrounding repatriation, once the benefits for both sides are understood, many medical schools might be only too willing to undertake repatriation work with our assistance."
APNZ mb