The walkout, involving over 1,400 staff, will start on March 31 and end on April 9, Easter Sunday, the union said, Reuters reported.
"It is the airport's workers who are fundamental to its success and they deserve a fair pay increase," Unite General Secretary Sharon Graham said.
The union said the airport's offer of a 10% pay increase could not make up for years of pay freezes and cuts.
In a statement, Heathrow said it had contingency plans in place to keep the airport running.
"Threatening to ruin people's hard-earned holidays with strike action will not improve the deal," a spokesperson for Heathrow said, adding that Unite should return to the negotiating table instead of striking.