NUJ members at the two papers, owned by Independent News & Media, voted 64% in favour of strike action in a postal ballot and by 80% in favour of action short of a strike.
At a meeting on Friday members decided to take action in the form of a mandatory NUJ chapel meeting on Friday 6 March between 5pm and 7pm. This coincides with the middle of peak production time.
The dispute is over plans by Independent News & Media to force through compulsory redundancies.
The publisher announced in November it would cut around 90 mainly editorial jobs from The Independent and The Independent on Sunday as part of a major restructuring programme that will affect all areas of operation.
The majority of the cuts will come from the editorial department but IN&M said "a sizeable number" of the redundancies will be voluntary.
However, since the November announcement IN&M has rejected requests by a number of staff to leave voluntarily and the NUJ has said it is concerned about a lack of strategic vision for the future of the newspapers.
Barry Fitzpatrick NUJ head of publishing, said: "We are today serving notice on the company of the chapel's intention to hold a mandatory meeting next Friday. At the same time, we are extending a further invitation to management to discuss ways to avoid compulsory redundancies.
"We are urging management to seek authorisation from Dublin for them to negotiate a sensible outcome to this dispute."
News of the strike follows reports at the end of January that Sir Tony O'Reilly has effectively put his Independent titles up for sale after pledging to dispose of "any loss-making businesses" as part of a drastic financial overhaul.
IN&M is understood to be open to discussions with potential buyers of The Independent and Independent on Sunday, which are believed to be losing at least £10m per year.
There have been reports that Russian businessman Alexander Lebedev, who recently bought a 75% stake in the loss-making Evening Standard for a nominal sum, is interested in the titles, which are now in housed in the same building in Kensington.
The Independent had average daily circulation of 215,504 copies in January 2009 -- a drop of 14.02% on January 2008.