Members of the National Union of Journalists, Bectu and Unite will walk out around mid-day on July 23, followed by a work to rule.
The opening ceremony for Glasgow 2014 will take place between 9pm and 11pm on Wednesday, July 23 at Celtic Park and is scheduled to be broadcast by the BBC.
The BBC holds exclusive rights to TV coverage of the Games in the UK. It is currently unclear what effect the strike will have on the screening of the opening ceremony.
The decision follows overwhelming votes in favour of industrial action in protest at an offer of £650 for those earning less than £50,000 a year and £500 for employees on more than £50,000.
Union leaders said staff had suffered five years of below inflation pay deals, adding that the BBC could afford to pay more.
Members of the NUJ voted by 77% in favour of a strike, while those in Bectu backed action by 79%.
NUJ general secretary Michelle Stanistreet said: "The decisive turnout and result clearly demonstrates that journalists across the BBC are not prepared to put up with paltry pay deals any longer, while those running the corporation continue to enjoy their lavish salary and perks at the same time as dishing out lectures about the need for staff to 'get austerity'."
Gerry Morrissey, general secretary of Bectu, said: "The BBC can find money for vanity projects, but cannot find money for its own staff, whose pay has dropped by 10% in the last five years."
Ms Stanistreet said: "When it comes to executive perks, lavish salaries for managers and jobs for their mates, the BBC executive is the board that likes to say yes.
"When it comes to paying journalists and programme makers that deliver the content that makes the BBC the envy of the world, the BBC has tried to peddle the line that a below-inflation deal is the only way of keeping their political and corporate enemies at bay in the forthcoming licence fee settlement.
"The NUJ believes there needs to be radical reform at the BBC, with executive pay capped at £150,000. That would free up the money to ensure fair pay for all staff.
"BBC managers have embarked on a major public relations exercise during the course of this ballot with one intention - to demonstrate that the NUJ is out of touch with its membership and that the disenchantment with the management of the corporation is only skin deep. Today's result demonstrates how badly out of touch they are."
The NUJ said its members were prepared to take "sustained action", warning that further dates for industrial action will be called if the dispute is not resolved.
Mr Morrissey said: "BBC rank-and-file staff are appalled at once again finding themselves at the back of the queue when managers sit down to review pay. Instead of playing to the political gallery, BBC senior management should have the courage to reward staff fairly for the increasing demands they face.
"Whilst the BBC's income has been at a standstill since Mark Thompson caved in to Government pressure in 2010, the BBC knows what its income is and has control over how it pays staff.
"BBC staff know what austerity means. They have accepted pay cuts for the past five years and are working harder and harder every year as staff numbers fall.
"Whilst BBC staff cherish the organisation they work for and have every respect for the licence fee payer, they have the same challenges as everyone else. They have to make ends meet and are entitled to expect that the value of their pay will be at least maintained."