ATLANTA — Inspire Brands, parent company of Arby’s, Sonic Drive-In, Buffalo Wild Wings and Rusty Taco, has agreed to acquire Jimmy John’s Sandwiches. Financial terms of the transaction were not disclosed.

Jimmy John’s operates more than 2,800 locations across 43 states. Following the completion of the acquisition, Inspire Brands will be the fourth-largest restaurant company in the United States with more than $14 billion in annual system sales and more than 11,200 restaurants across 16 countries.

“Jimmy John’s is a great fit for the Inspire family,” said Paul Brown, co-founder and chief executive officer of Inspire Brands. “What started in 1983 as a sandwich shop in a converted garage in Charleston, Ill., has grown into a national, differentiated brand with a passionate fanbase. We are excited to welcome the Jimmy John’s brand to Inspire and look forward to working with their team and franchisees to help the company achieve its next stage of growth.”

The transaction is expected to close by the end of October. James North will become president of the Jimmy John’s brand, reporting to Mr. Brown. Jimmy John Liautaud, founder of Jimmy John’s, will step down as chairman of the board and transition to an adviser for the brand.

“Jimmy John’s has found the ideal home at Inspire,” Mr. Liautaud said. “Inspire’s long-term approach, culture of innovation and commitment to helping brands grow sets it apart from the rest. I couldn’t be prouder of the company we’ve built, and I can’t wait to see what Jimmy John’s is able to accomplish under Inspire’s leadership.”