The ballot began last month over a pay dispute involving about 4,000 staff who have joined the airline since 2010 on "Mixed Fleet" contracts.
More than 2,000 workers were balloted about the action, which will take place at Heathrow Airport after December 21, Unite union has confirmed.
Tunout in the ballot was 60 per cent. The union will meet in the coming days to finalise dates.
Tensions have been running high this year among the mixed fleet staff who claim they were promised far higher rates when they joined BA.
The union claimed earnings were advertised between £21,000 and £25,000 but in reality started at just over £12,000 plus £3 an hour flying pay.
Matt Smith, regional officer for Unite, said British Airways' pay rate are "indefensible" and the crew are at a "breaking point"
He said: "Not only are the pay rates indefensible but, in aviation, low pay is a safety issue. Thirty per cent of the Mixed Fleet crew have been with the company for just under a year.
"Crew simply can't afford to stay. Inexperience, fatigue, and the fact that BA recently cut the length of crew training courses means Unite is genuinely concerned about the potential repercussions.
"We urge British Airways to avoid this dispute and do the right thing by both the frontline staff and the travelling public, by engaging with Unite to negotiate a genuinely meaningful way forward."
A spokesman for BA said the company was "extremely disappointed" that the union is creating uncertainty for the airline's customers.
Biggest business scandals in pictures
Biggest business scandals in pictures
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"Mixed Fleet Unite represents about 15% of our cabin crew. We remain focused on resolving this issue as quickly as possible without any disruption to customers.
"We have proposed a fair and reasonable pay increase to Mixed Fleet cabin crew which is in line with that accepted by other British Airways colleagues and which will ensure their reward levels remain in line with cabin crew at our airline competitors."
The announcement comes as the UK remains in the grip of a walkout by Southern Rail workers that has caused chaos for hundreds of thousands of passengers.Reuse content