Both vessels have technology able to detect underwater signals emitted by data recorders.
In addition, a dozen military aircraft and 13 ships are already searching three areas about 2,000 km (1,240 miles) north-west of the Australian city of Perth.
They will cover some 216,000 sq km on Sunday.
Flight MH370 disappeared en route from Kuala Lumpur to Beijing four weeks ago with 239 people on board.
The plane is believed to have crashed in the southern Indian Ocean, although no confirmed debris has been found.