The company said it plans to add another 10 to 15 franchises in South Yorkshire and Derbyshire, thereby growing to 69 stores in the area.
It said the expansion would create 350 jobs, but did not specify how many of these would be in Yorkshire.
The move follows a visit by Subway co-founder Fred DeLuca when he announced plans to increase its UK stores to 2,000 from 1,435, creating 6,000 new jobs.
Husband and wife team Rachana and Kiran Pancholi will lead the growth in South Yorkshire.
“The planned expansion across the region will not only provide a significant boost to the local employment market but also give entrepreneurs the opportunity to establish their own small business in the area,” said Mrs Pancholi.
Mr Pancholi added: “Rachana and I are delighted to have the opportunity to grow the business in South Yorkshire. Sheffield in particular has seen extensive development over the past decade and we are pleased to be playing a part in future growth across the county.”