One hundred council IT staff, who are members of the public sector union Unison, voted 91% in favour of industrial action, said Pat Kerry, lead negotiator on the council's Bradford-i outsourcing project.
An all-out strike was planned for Thursday and Friday, with selective action on Saturday, Sunday and Monday, said Kerry.
Last month the council increased the number of IT staff threatened by redundancy to 40 as a result of its 160 million outsourcing deal with Serco, according to Unison.
Kerry said the council was in negotiation with the union and a solution could be close.
"I think we are nearly there, but we have to gain political approval," he said.
A Bradford Council spokesperson said, "We regret that the staff have decided to take industrial action over the implementation of Bradford-i.
"Discussions are still ongoing with the trade unions involved and staff to seek a resolution on this."