Dr Lorraine Eade, chair of Ngāti Rārua o Te Wairau Society, which now owns the item, said its significance was “beyond measure”.
She said its return was an opportunity to acknowledge Cleghorn’s work for Māori people.
The doctor advocated for their right to attend a local hospital instead of being required to travel further afield for medical treatment, Pitt Rivers Museum said.
He also spent time educating families at their homes on the importance of taking public health measures, it added.
Shane Graham, chief executive of Te Rūnanga o Ngāti Rārua, a Māori authority, said the return was a momentous occasion.
“It restores mana [prestige] and honours the deep emotional and cultural significance of our living connection to this taonga [treasure],” he said.
Prof Laura Van Broekhoven, director of the Pitt Rivers Museum, said: “We are very pleased that the day has come for the Kahu Kiwi to return home.”
A ceremony was held in Oxford earlier to mark the cloak’s departure.