Members of Unison and GMB have backed industrial action in protest at a 1% pay offer.
Police community support officers (PCSOs) and fingerprint experts are among those who voted for the action.
The unions want a 3% increase in wages and complain about staff facing a pay freeze or below inflation rises for the past three years.
Unison members voted by around 60% in favour of strikes.
Other police staff members balloted included 999 call handlers and custody and detention officers.
Unison general secretary Dave Prentis said: "These results send a clear message that after two years of pay freeze and last year's below inflation pay rise, police staff have had enough and that they are now ready to take industrial action over pay.
"We are calling on the police employers to return to the negotiating table to improve the current pay offer."
The union's police sector committee is set to meet to consider the ballot results, and discuss the next move.
Members of the GMB union also voted in favour of strikes, and national officer Sharon Holder said: "Following the conclusion of the ballots, unions will now meet and announce the planned industrial action."
Civilian staff across police forces in England and Wales have voted to strike in a row about pay.