At a meeting of Falkirk Council, members agreed a new structure which will see the Trust's functions being split into three of the council's directorates.
Culture, arts, museums and parks will move to the newly formed Place division; libraries will move under the umbrella of Housing and Communities; and sport and leisure will move to Children’s Services.
It is expected that work to transfer all services will be completed by April 1, 2022.
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A number of task groups involving both Council and Trust staff have been set up to take forward the work involved in the transfer, working on areas such as asset transfer; finance; human resources; charity status among others.
A project management group, involving senior staff from the Council and the Trust, has also been established to oversee this work.
“Planning has already started on the various pieces of work that are needed to make the transfer successful.
“Everything possible is being done to ensure we get the most from the new arrangements and that our communities and visitors continue to receive a positive experience.”
The Labour group, which opposed the Trust being brought back in-house, was particularly unhappy that Libraries were to come under housing and communities.
Labour group leader Robert Bissett quoted a letter from the Trust's chief executive, Maureen Campbell, who had expressed the board's concerns that the core function of libraries would be lost.
Both SNP and Conservative members, however, said that bringing libraries into the communities department would allow them to be used in lots of new ways that would make their services even more valuable to local people.
Following a vote, Labour's proposal to keep libraries with the rest of the cultural services was rejected.
Last week, Maureen Campbell announced that she was standing down as chief executive.
Members paid tribute to her work over the years leading several major projects, and helping to build the Trust.