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Australia's former Deputy Prime Minister Barnaby Joyce has won back his seat, just a month after being ruled ineligible over a dual citizenship row.

He was disqualified when it was revealed he held dual Australian-New Zealand citizenship.

But he has since renounced his New Zealand citizenship, and on Saturday won the by-election in New South Wales.

The dual citizenship crisis has cost nine MPs, including Mr Joyce, their seats and the government its majority.

Counting was still under way on Saturday when Australia's national broadcaster ABC declared that Mr Joyce had "easily won" the by-election.

It was called to fill the seat Mr Joyce left vacant when a High Court of Australia ruling forced him from office. Under constitutional rules, MPs must be citizens of Australia alone.

He has since rescinded his New Zealand citizenship, claiming he never knew he had inherited it from his father.

Voters did not hold the slip against him, as ABC predicted he would win with more than 60% of the vote - more than the share he received at the last general election.

"Barnaby Joyce has been elected with what appears to be a record in the history of by-elections in Australia," local news outlets quoted the prime minister, Malcolm Turnbull, as saying.

The election result is welcome news for Mr Turnbull's government, as it restores a slim majority in the House of Representatives.

It lost its outright majority in the house when former tennis star John Alexander stepped aside in November over suspected British dual citizenship.