The ballot, which began in November, is in response to 99 proposed redundancies at the mill, as well as its imposed selection criteria for redundancies and what members claim are inferior severance payments.
Peter Ellis, Unite national officer, said: "This result demonstrates the depth of resentment and frustration felt by our members at the way the company and local management have handled the proposed closure of a board machine identifying a loss of 99 jobs."
He said the union was looking forward to "realistic and constructive discussions" at a mill conference on Friday (11 December).
"The company has now agreed to the conference having said they didn't see the point in meeting with us within the national agreement procedure," he added.
The union claimed that company bosses have refused to follow dispute procedures and that negotiations over the planned redundancies have failed.
In October last year, it was announced that 99 employees at the 484-staff Iggesund mill were to be made redundant as part of plans to close one of the company's two machines.
Iggesund Paperboard is a member of the Holmen Group and manufactures high-quality virgin fibre paperboard for the packaging and graphics sectors.
Michael Hunter, Iggesund Paperboard (Workington) human resources manager, said: "For some time, we have had a meeting planned with Unite representatives, in line with recognised procedures for avoiding disputes.
"It's therefore not appropriate to comment on the situation in advance of this meeting."