The plans follow two consultations earlier this year and mean original proposals to close six of the borough's nine libraries have been thrown out.
Three of those six libraries – Donnington, Dawley and Stirchley – will now be run by town or parish councils.
However, no organisation has come forward to help fund or run the mobile library service, which will now end from March 31 next year.
A fourth library in Hadley library will be run by Hadley Learning Community, supported by Hadley & Leegomery Parish Council.
The council will continue to run Newport and Madeley libraries with some changes to opening hours. These libraries, along with those at Southwater and Wellington, all provide a First Point service for the community to use, and all four libraries will continue to be run by the council.
In Oakengates, the library will also be run by the council with some revised changes to opening hours. Oakengates Town Council has also agreed to fund the opening of the library on Saturday mornings.
Telford & Wrekin Council's cabinet will discuss the plans at a meeting on Thursday.