Both Broseley Library and Albrighton Library will no longer be run by Shropshire Council from February 27. Broseley Town Council and Albrighton Parish Council have agreed to take on their libraries and customer service points from Shirehall.
But both libraries will close for at least six weeks for work to be carried out to move each council's offices in. Mobile libraries will be made available outside both buildings on every Saturday in March from 10am until 1pm.
The two libraries were among several earmarked for closure by Shropshire Council as part of cost-cutting measures unless alternative groups could be found to take them on.
Trudi Barrett, clerk of Broseley Town Council, said: "The town council's move into the library provides a great opportunity to bring together services in the town.
Recent consultation showed overwhelming support for the town council taking on management of the library service, customer service point and car park."
People can still borrow books as normal until February 27. Then the books may either be returned to another Shropshire Council library or be kept until their library reopens.