It confirmed Harold Martin of the anti-independence Future Together Party as new president and the pro-independence politician Gilbert Tyuienon as vice-president.
The two were this year elected three times before but their administration collapsed every time within minutes because the Caledonia Together Party resigned from the collegial body.
The resignations came amid an unresolved dispute over which flag the territory should choose ias part of its decolonisation process.
France has been scrambling to change the electoral law to give any new government an 18-month grace period in a bid to stop the serial resignations.
The French high commissioner says he hopes this government will be stable.
The next general election is due in three years.