Members of the Communication Workers Union (CWU) backed strikes by 98.7% on a turnout of more than 72%.
It was the second ballot of Royal Mail workers, who are already planning to strike on August 26 and 31 and September 8 and 9 in a separate row over pay.
CWU general secretary Dave Ward said it was a "staggering" result which sends a clear message to bosses about opposition to plans to changes to terms and conditions under modernisation plans.
"We will do everything possible to see if we can make progress but the Royal Mail management has to change its position," Mr. Ward said.
"If they don't, then we will take strike action."
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