In a statement, Goodyear said: "The decision by the workforce means that it will be extremely difficult to build a future for the plant."
Trade unions, who had recommended the deal to members, spent 11 months in negotiations with Goodyear management. The agreement, rejected in a ballot by four votes to one, would have limited job losses to 300 in exchange for workers accepting a cut in pay and additional work.
Roger Shutt, regional industrial organiser of the Transport and General Workers Union, described the vote as a choice between "the plague or cholera".
He added: "We are not going to lie down and die - we will still battle for the jobs of our members."