After taking soundings from shareholders representing more than 40 per cent of Z's shareholders, Z said the offer was within a range that the board was willing to recommend.
"The Z board believes that the scheme represents fair value for Z shareholders," Z Energy chair Abby Foote said.
Shareholders are expected to vote on the deal early next year, with Ampol hoping to complete the transaction by the middle of 2022.
Z Energy shares jumped around 7 per cent on the news to $3.60, below the scheme of arrangement but possibly reflecting the more than six months shareholders would have to wait for the takeover to be completed.
Formed from the sale of Shell's downstream assets to New Zealand investors in 2010, Z Energy became by far the largest fuel company in New Zealand when it purchased Chevron's New Zealand business, Caltex, in 2016.
The combined group has 481 petrol stations and accounts for around 40 per cent of New Zealand's fuel sales, as well as import terminals around New Zealand.
As well as shareholder and High Court approval, the scheme requires approval from both the Commerce Commission and Overseas Investment Office.
On Monday Ampol, which has owned discount company Gull since 2017, has committed to selling its existing New Zealand assets in order to gain regulatory approval. Previously it had only flagged a possible sale of Gull.
Mike Bennetts, who has been chief executive of Z Energy for more than a decade, said the company had used the past six weeks to satisfy itself that the transaction was likely to get approval. Early meetings Z had attended between Ampol and the Commerce Commission had raised "nothing unexpected" Bennetts said.
"We satisfied ourselves that this was the sort of thing we should recommend to our shareholders with a high degree of confidence of securing the necessary approvals," Bennetts said.
There had been a wide variety of feedback from shareholders on the Ampol offer but overall he believed it worked for shareholders.
Ampol said the takeover would create a trans-Tasman fuel champion with around 2400 petrol stations and 23.5 billion litres of fuel sales a year.
Managing director Matt Halliday said the deal could lead to up to $80m in synergies however this would come mainly from its fuel import and refining infrastructure in Australia.
"Z Energy will operate largely independently, as a subsidiary of Ampol, with the Z Brand maintained and retention of key personnel a priority."