The change, agreed at a meeting of full council today (Oct 1), will give the council greater flexibility on how the centres are managed and potentially accelerate its leisure improvement programme.
All staff employed at the centres will transfer on their existing pay and conditions to the new 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 will enable the smooth continuation of services while the council is reviewing how sport and leisure should be provided across the district.
Leader of SKDC, Cllr Kelham Cooke, said: "Part of our role as a district council, as community leaders, is to support our residents and local businesses through current challenges, whilst keeping a forever watchful eye on the future, to ensure that our recovery in South Kesteven is as strong as possible.
"That means enabling viable businesses to operate, providing a vital service for our communities, and demonstrating value for money for our taxpayer.
"Financially, it would not offer value for money for council taxpayers to either extend the current contract or go to the market. It is simply not the right time.
"But leisure facilities are part of the fabric of strong and healthy communities, so I believe there is a sound business case for bringing leisure in-house with the creation of LeisureSK, and an ethical duty to support the wellbeing of residents of all ages and all demographics.
"By creating LeisureSK, we will be more in control of our future leisure provision and that can only be good for the council, the staff who will join us and those who use our leisure centres."
The council is 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 Cooke said: "Bringing the leisure centres under the control of the council gives us greater flexibility at a time when we are committed to developing and investing in them.
"Our plans 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.