One item was found on a sandbank by an amateur US investigator in late February and the other in December by a South African tourist.
MH370 disappeared in March 2014, en route from Kuala Lumpur to Beijing, carrying 239 passengers.
Despite a huge search, only one fragment of the plane has been found.
The Australian Transport Safety Bureau (ATSB) confirmed to the BBC that they had received the debris from Mozambique on Sunday and were "working with the Malaysian investigative team to analyse it".
Malaysia's transport minister has previously said there is a "high possibility" the debris found in February came from a Boeing 777, the same model as missing Malaysia Airlines flight MH370.
Australia is leading the search for the plane as it is suspected to have gone down in waters closest to the country.
Specialists from Boeing are assisting in the analysis work.
So far, the only debris confirmed by investigators to have been from the missing plane is a fragment of wing found on the Indian Ocean island of Reunion.
Another piece of debris found recently on the island is unlikely to have been from the missing plane, Australian investigators have said.
The location where the various pieces of debris have been found is consistent with models of ocean currents, which show where the sea might have carried wreckage from the suspected crash site.
Two pieces of debris found in Mozambique which may have come from missing Malaysia Airlines Flight MH370 have arrived in Australia for analysis.