The Employment Relations Authority's recommendations for 2022 was a 5 per cent pay increase and a $4000 lump sum payment, for 2023 a 4.5 per cent increase and a $3000 lump sum and in 2024, a 4 per cent increase.
Under the authority's recommendations, the agreement will expire in July 2025.
Essity had previously said it was offering rises of 3 per cent per year plus a one-off cash payment in the first year.
The union wanted rises to match inflation, and said its position was based on analyst predictions of a 15 per cent total rise over three years.
Kawerau is the last remaining paper production and manufacturing plant in the country supplying nearly 50 per cent of the market – the rest is made from imported paper.
"Essity's sole focus has been on reaching an agreement that is fair but helps secure the long-term future of the Kawerau mill," today's statement said.
Economic pressure had seen one other major plant close over last year and another reduce jobs and pay rates to stay competitive. In the past 12 months, two other suppliers had left New Zealand because of cost pressures.
Essity said it had shown its commitment to the Kawerau mill by investing $130m in plant upgrades over recent years.
A Pulp and Paper Workers Union media statement said it received notice "via the media" that Essity had accepted the Employment Relations Authority's recommended pay offer, which followed several days of facilitated bargaining.
Union secretary Tane Phillips said members would discuss the deal tomorrow morning.
"Members will vote on the offer tomorrow morning and we will make a further statement following that meeting."