Lung transplants from living donors usually involve transferring the inferior lobe which has greater breathing capacity.
But a middle lobe was transplanted in this case as it is smaller than an inferior lobe and is of the right size for the boy, the Okayama University Hospital said.
The boy and his mother were not identified.
The transplant of a middle lobe is seen as difficult, said the university in western Japan.
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"We deem that the operation has been successful," it said.
The hospital said earlier that a successful operation would be the first of its kind in the world.
The surgery started at 1:35 pm and the boy started breathing with the transplanted lung about five hours later, the statement said.
The boy is the youngest lung recipient in Japan, the hospital said.
He underwent a bone-marrow transplant for leukaemia about two years ago but later developed graft-versus-host disease, a complication in which the newly transplanted material attacks the recipient's body, Kyodo News said.