Under strict election day laws New Zealand does not allow exit polls during voting, which opened at 9am (2100 GMT Friday) and closed at 7pm (0700 GMT).
However, a firm indication of the outcome is expected within about three-and-a-half hours after the end of voting.
There were 3.2 million registered voters, of which 1.24 million cast an early vote.
The campaign has been the country’s most volatile in recent memory, with momentum swinging from English to Ardern and then back again.
If neither English, whose National Party is seeking a record-equalling fourth consecutive term in power, nor Ardern can form a government outright, or with the help of minor support parties, the New Zealand First Party of populist anti-immigration campaigner Winston Peters looms as the potential kingmaker.
No party has claimed a majority government in New Zealand’s 120-seat parliament since proportional voting was adopted in 1996.