Three-quarters of GMB members balloted voted for industrial action over collective bargaining rights at the depots.
GMB general secretary Paul Kenny said: 'GMB members have voted three-to-one to take strike action, despite all the company's attempts to dissuade or intimidate them to vote no.'
The GMB wants to establish national bargaining structures with Asda over pay, conditions and union facilities at the distribution centres. The union also said it wanted the supermarket to pay last year's unpaid£300-a-worker bonus.
The union said it would take legal action if Asda employed agency staff during any strike.
GMB shop stewards will meet in Manchester tomorrow to set dates for industrial action. It is thought the strike could take place during the busy World Cup quarter finals weekend.
Asda people director David Smith said: 'It makes us really sad the GMB's threatening strike action when there's already a great offer on the table that could lead to collective bargaining at all our depots, if that's what the majority of our colleagues tell us they want. If the GMB wants to talk, we're always willing to get back round the table.'
The grocer said it would do everything 'lawfully possible' to ensure customers are not affected by the industrial action.