About 120 members of Unite, at two DHL sites in Tickhill, South Yorkshire and in Harworth, Nottinghamshire will walk out initially on 15 May.
Harriet Eisner, of Unite, said it was over "a derisory pay offer of 1.25%" and the closure of the Harworth site.
DHL said it was "disappointed" about the strike action and would try to minimise any disruption.
DHL Supply Chain urged the union to return to negotiations and said the planned closure of Harworth followed a customer decision to transfer to a "new provider".
"We have not only met, but exceeded, our legal obligations to our workforce", the company said.
Many of the 150 workers at the threatened site faced losing their jobs, Unite said.
The workers who voted to strike for 24 hours on 15 May, have also backed walkouts for three days on 25 May, and for 11 days from 1 June, it said.
DHL has operations in more than 220 countries and has an international workforce of more than 350,000.
Warehouse workers at three depots of delivery firm DHL are set to stage 15 days of strikes, it has been announced.