The Bectu union said industrial action was "the only option left open" and that strike dates would be publicised to avoid inconveniencing visitors.
According to The Stage, 38 tour guides at the venue are Bectu members.
A Globe spokeswoman told the paper the venue had "made all reasonable efforts to avert industrial action".
According to The Stage, tour guides had been seeking a pay increase that would have raised their hourly rate from £11.24 to £13.50 an hour.
The two parties met at Acas - the Advisory, Conciliation and Arbitration Service - earlier this month but were unable to reach agreement.
"We had hoped that management would take seriously the opportunity we offered to them to avoid conflict," said Bectu's Pat Styles.
"Unfortunately, management representatives failed to grasp this opportunity, preferring instead to first offer our members what was effectively an insulting cut in pay and then refusing to accept various solutions we offered to them."
"The Globe maintains that a benchmarking exercise is the only viable means of establishing an appropriate rate of pay for guides that is consistent with our organisational policy to pay at industry median levels," the popular tourist attraction's spokeswoman told The Stage.
"We are still open to further consultation... and will in any case be undertaking a salary benchmarking exercise for all Globe staff, including the guides, over the summer as originally planned."
The Globe's representative is quoted as saying that audio guides will be made available on days when there is a strike.
The news follows an announcement on Tuesday that workers at the Royal Opera House in London are to vote on whether to take strike action over pay.
Tour guides at Shakespeare's Globe in London are to take industrial action after talks to resolve a pay dispute broke down.