The hike - which is expected to be signed off by ruling cabinet members - will mean the base rate for standard residential care will stand at £652.82 a week, rising from £607.44.
For dementia sufferers, the weekly charge will be £708.65 - a rise on the previous fee of £654.94 - or £36,849.80 annually.
A council report said: “In 2019, the council developed a cost of care model for determining the average cost of delivering residential care in Barnsley.
“The cost of care model was shared with the Barnsley Independent Care Home Association as part of the council’s consultation on fees.
“The association has previously rejected the costs of care model’s fees, however fee rates based on this model have been accepted for 2022/23.
“Following discussions, the council has now reached an agreement on a 10.6 per cent increase in the fees for residential and nursing care.
“The agreed fee rate for 2022/23 reflects the 6.6 per cent increase in national living wage and takes account of other cost pressures such as the 1.25 per cent National Insurance levy, inflation and energy costs.
“There is no standard methodology for agreeing annual uplift - it is based on individual requests from providers and agreed on a case-by-case basis.
“However, work is currently ongoing with providers to establish a framework contract and an approach to determining fees.
“Concerns continue to be expressed, in discussions with care providers, regarding the council’s fee rates and the impact on capacity and market sustainability.
“This means that the council needs to consider market costs and other pressures facing providers in setting fees and deciding on annual uplifts.”
The care sector - which was responsible for a stand-off between the council and the association due to the local authority’s ‘Excellence In Care’ scheme which asked providers to pay staff £1 more than the national living wage - has faced staffing issues owing to the pandemic and wages.
It was envisaged the pay rise - agreed by the council as part of last year’s budget - would help retain staff and encourage more to begin a career, as well as address the ‘transient’ nature of employee turnover in the industry.
It’s estimated the rise to £9.72 an hour equates to an annual increase of around £3,000 a year for workers.
A total of 31 out of 43 care homes in the borough have implemented the scheme - almost three-quarters of facilities.
The report added: “Providers have shared their concerns around the high levels of staff turnover, recruitment and retention, stating that they may be unable to meet the demands for good quality care as specified in the contract.
“Some homes continue to reject the enhanced rate for affordability reasons due to the balance of council-funded and self-funded people they support.”