The so-called Crown offices - the larger branches usually found on high streets - will be franchised to the retailer by next April.
The Post Office is planning to franchise 70 Crown offices, a move which has led to a series of protest strikes by the Communication Workers Union.
The 16 are located across England, Wales and Scotland, with the Post Office saying they will offer the same range of services, with longer opening hours, mostly over seven days a week.
Kevin Gilliland, network and sales director at the Post Office, said: "The investment in our Crown network is a significant milestone in our plans to turn around our business. We are changing the way we do business across our network, introducing new, more modern branches and making it as easy as possible for customers to access our services.
"We are already well known for our mail and government services, but we are also growing rapidly in financial services, providing customers with a serious alternative to high street banks.
A union spokesman said: ""Franchising post offices to companies like WHSmith has been proven to reduce the quality of customer service and there are often issues with access arrangements for those with buggies, wheelchairs or mobility issues. In addition, the last time WHSmith took on post offices they weren't interested in employing the long-serving, experienced post office staff, with hundreds losing their jobs as a result. CWU challenged this in court and TUPE will now apply.
"It's deeply disappointing that further franchising is being considered when there are so many negative connotations linked with this model. Staff and customers alike will be concerned at this news."
The branches moving to WHSmith are in:
- Kings Heath
- Stockton on Tees
- Sutton Coldfield
- Swiss Cottage
- West Wickham