Sonic is the latest U.S. restaurant to be taken private. Zoe's Kitchen was taken private by Mediterranean restaurant chain Cava last month, while NRD Capital took Ruby Tuesday private in October last year for about $335 million.

The deal comes as Sonic battles intense pricing competition from bigger rivals such as McDonald's Corp and Wendy's Co. The company's same-restaurant sales have fallen for at least the past two years.

Inspire's offer values Sonic at $43.50 per share, a 19 percent premium to the stock's Monday close. Sonic's shares were trading at $43.35.

Including debt, the deal is valued at about $2.3 billion, the companies said.

Inspire Brands was formed by private equity firm Roark Capital as a holding company when Arby's completed the acquisition of Buffalo Wild Wings earlier this year.

Roark, which also owns bakery chain Cinnabon, bought a majority stake in Arby's from Wendy's Co in 2011 and purchased the remaining 12.3 percent last month.

Guggenheim Securities LLC is the financial adviser to Sonic, while Shearman & Sterling LLP is its legal counsel.

White & Case LLP is Inspire's legal counsel.

(Reporting by Uday Sampath in Bengaluru; Editing by Sriraj Kalluvila)