Under the proposals all staff employed at the centres will transfer on their existing pay and conditions to a new wholly owned council company called LeisureSK.
The council's contract with management company 1Life, who currently operate the centres at Grantham, Stamford, Bourne and Deepings, is due to end in the New Year.
Moving the operation to LeisureSK provides a short to medium term solution that will enable the smooth continuation of services while the council is reviewing how sport and leisure should be provided district-wide.
Leader of SKDC Cllr Kelham Cooke said: "Leisure services play a key role in helping to maintain the physical and mental wellbeing of our residents. We have embarked on a leisure improvement programme that will support this and the new arrangement will give us full control over it.
"In addition, the formation of a new company for the council means the service will have the backing and support of a major employer, experienced in delivering a wide range of services. The transfer of existing staff at the leisure centres to LeisureSK will mean that the company retains their knowledge and expertise."
The council is currently undertaking feasibility work on providing a new leisure centre for the Deepings and is looking to make major improvements to its other leisure facilities.
Cllr Barry Dobson, SKDC's Deputy Leader and Cabinet Member for Growth and Leisure, said: "We have had a long and successful partnership with 1Life but, with our current contract due to end in the New Year, this is an appropriate time for a change.
"As a council we are committed to investing in and developing our leisure facilities, which will have a positive impact on the wellbeing of residents by helping them to be active and stay healthy."
All leisure centre memberships and bookings will remain in place and the centres will continue to operate within Covid-19 guidelines.