Sport England is funding the routes in the Bewsey and Dallam areas of the Cheshire town, where high numbers of people do not have their own transport.
Seventy-nine families have already taken advantage of the initiative to encourage them to take up swimming.
The idea has received ??230,000 funding from Sport England's Community Activation Fund.
Warrington Borough Council backed community leisure operator LiveWire's application for the money, which finances transport to Great Sankey Leisure Centre - four miles (6km) away from Bewsey and Dallam.
Families who have children in three local schools will benefit from free travel for three years.
Mike Diaper, Sport England's director of community sport, said: "We know there is a significant gap between the number of people playing sport for those in low socio-economic groups and those with higher incomes.
"We also know from our insight that there is high demand for sport from people who earn less."
Councillor Kate Hannon says people in those areas are "sometimes the forgotten few".
Ms Hannon, who is responsible for leisure at the council, said: "By providing facilities that they can access it is a stepping stone for them to give them more confidence themselves.
"Dallam has no access to GP services or any other health services."
A planning application is due to be submitted in August for the demolition of Great Sankey Leisure Centre.
The council wants to replace it with a "neighbourhood hub", which would include a swimming pool.
Free buses are being laid on to take people from two of the most deprived parts of Warrington to a swimming pool.