A 52% majority of Unite members accepted the terms of the agreement, which is between Unite and the Confederation of Paper Industries (CPI).
The vote will affect around 3,000 Unite members working in 18 different companies throughout the UK.
Peter Ellis, Unite national officer, said the closeness of the vote reflected "a large degree of dissatisfaction" with the level of settlement.
He said: "However, the fact that we had a majority in favour indicates that our members recognise the below zero RPI and the delicate state of the paper manufacturing industry."
Ellis added he was confident that all conforming companies would meet the award in full.
He said: "We can look forward to a year of job stability in the paper manufacturing industry."