Further, Australia would provide technical assistance to the Malaysian government and Ocean Infinity.
Malaysia is negotiating a "no find-no fee" deal with a U.S. company to renew the search for downed flight MH370.
Chester said that the Ocean Infinity search will focus on the 25,000sq km area that was flagged by the investigators in recent months.
However late previous year the Minister for Infrastructure, Darren Chester, said any resumption of the search required precise identification of the final resting place of the wreckage.
Australian Transport Minister Darren Chester on Friday announced the deal between Ocean Infinity and the Malaysian government. Its conclusion said the location of MH370 could not be pinpointed, despite a large-scale search of about 300,000 square miles of ocean.
MH370 was carrying passengers and crew from 14 different countries when it disappeared, most from China and Malaysia.
In August, when Ocean Infinity first tabled the offer, it declined to reveal the exact terms of the proposal, but said in an email at the time to CNN that it was willing to "take on the economic risk of a renewed search".
"I hope that this new search will bring answers, both for the next of kin and for the rest of the world".
Australia, China and Malaysia, which jointly coordinated and funded the search operation, had in January suspended the search for MH370 when traces of the Boeing 777 could not be found in the 120,000 sq km search area of the southern Indian Ocean.
MH370 debris recovered from the beaches of the French island of Reunion, Mozambique, Mauritius, South Africa and Pemba Island (Tanzania), as confirmed by lab analyses, showed that the plane crashed in the sea and gave rise to new hypotheses about the incident that occurred.
"Given the high confidence in the search undertaken to date, the experts agreed that the previously defined (search) area is unlikely to contain the missing aircraft", a spokesman for the Australian Transport Safety Bureau (ATSB) said in a statement.
The ATSB released its two final reports on the search earlier this month. The Texas-based explorer will search various sections of the Indian Ocean for additional wreckage from Flight 370, which disappeared on March 8, 2014.