The offer price represents a 30.1 per cent premium to Pushpay's "undisturbed" share price of $1.03 per share on April 22 this year.
Since then, the ASX All Technology index has declined 12.1 per cent and the NZX50 has declined 6.8 per cent.
The stock traded last week at $1.19.
The deal gives Pushpay an implied equity value of US$898 million, or NZ$1.539m.
The scheme is subject to Pushpay shareholder and court approval, regulatory approvals and other conditions.
Pushpay shareholder approval will be sought at a special meeting expected to be held early next year.
"Pushpay shareholders do not need to take any action at the current time," the company said.
Chairman Graham Shaw said the deal followed receipt of various unsolicited, non-binding expressions of interest to acquire the company.
Pushpay offers a platform through which American churchgoers make donations over their mobile phones.
"In considering the options, including the possibility of continuing to implement the company's growth strategy as a publicly listed company, the board adopted a long-term view of the risks and rewards of various alternatives," he said.
"After a thorough assessment, the Board believes that the Sixth Street/BGH Consortium Scheme proposal currently represents the most compelling value for shareholders.
"Although the board remains confident in the future of Pushpay, the transaction will accelerate a capital return to shareholders and mitigates the risks that would otherwise be involved in delivering the opportunities from executing Pushpay's strategic plan over time," he said.
Shaw said the board had unanimously recommended the transaction to shareholders.
The company went into a trading halt, pending an announcement, last week.
Trade is due to resume this morning.
Separately, Pushpay provided a trading update and preview of results for the first six months of the financial year ended September 30 and revised down its guidance for the full financial year to March 2023.
The results included a full six months trading from Resi Media, acquired in August 2021.
Pushpay expects operating revenue of US$103.0 million for the six months up 10 per cent on the prior comparable period.
For the full year, the company said it now expects to be at the lower end of its previous 2023 underlying ebitdaf guidance of between US$56.0m and US$61.0m.
The company has now revised its guidance range for Underlying ebitdaf to be between US$54.0m and US$58.0m.