Under the proposals, post offices in six towns will be closed and re-open as counters in WHSmith stores. Employees will be offered the opportunity to relocate to other Post Offices, or take voluntary redundancy.
The Communication Workers Union (CWU), which represents affected workers, said the deal would affect at least 125 jobs.
CWU assistant secretary Andy Furey said: 'Valuable public services and skilled staff are being lost to inexperienced retailers that refuse to take Post Office employees.'
A WHSmith spokeswoman said the workers were 'fully able and welcome to apply for the jobs at WHSmith'.
Protestors will picket WHSmith's stores in Slough, Altrincham, Shrewsbury, Swansea, Hammersmith and Ashton Under Lyme.
The CWU is balloting 500 members on strike action to take place later this year. A result is expected on August 23.