Flight MH370, a Boeing 777, was carrying 227 passengers and 12 crew, including six Australian citizens and one New Zealand resident of Western Australia, when it vanished on its way from Kuala Lumpur to Beijing in 2014 in one of the world's greatest aviation mysteries.
The decision would enable seabed search operations to begin in a new location estimated to cover 15,000 square kilometres in the southern Indian Ocean, based on a "no find, no fee" principle, Transport Minister Loke Siew Fook said.
Ocean Infinity would receive $US70 million ($A111 million) if the wreckage was found, he said.
"The government is committed to continuing the search operation and providing closure for the families of the MH370 passengers," Loke said in a statement.
The government in December said it had agreed in principle with Ocean Infinity's proposal to resume the hunt for MH370.
The firm had conducted the last search for the plane that ended in 2018 but failed on two attempts.
Those followed an underwater search by Malaysia, Australia and China in a 120,000 sq km area of the southern Indian Ocean, based on data of automatic connections between an Inmarsat satellite and the plane.
A ship that will look for the missing plane was deployed to its Indian Ocean search zone in late February, ship tracking data showed, even though a deal had yet to be signed with the government.
It was not immediately clear how long the search contract with Ocean Infinity would be.
Loke had previously said it would cover an 18-month period.
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