About 600 workers were laid off last December after the U.S.-based company closed its plant in Stadacona, Que.
If the union members accept the proposal the company says the mill could resume operations within a month.
The union rejected an earlier offer which it says would have slashed wages and pension benefits.
Workers at company's plants in Riviere-du-Loup and Gatineau will also be asked to vote on Monday and Tuesday.
White Birch was the second-largest newsprint manufacturer in North America when it filed for bankruptcy protection in February 2010.
At the time it had about 1,300 employees at three pulp and paper mills and a saw mill in Quebec, as well as a fourth pulp and paper mill in Virginia.
The company manufactures high quality newsprint, directory paper and paperboard.