Shares in the health food-focused supermarket chain shot up more than 23% after the announcement.
The Fresh Market- which has 186 stores across the US - said in October it was looking for potential buyers.
The Fresh Market's founder, Ray Berry, and his son Brett Berry agreed to roll over their 9.8% stake in the company and will stay on after the purchase.
The Fresh Market's chief executive officer, Rick Anicetti, said the deal "recognises the value of The Fresh Market's strong brand and significant growth prospects, while providing stockholders with an immediate and substantial premium".
Apollo will pay $28.50 a share, a 24% premium on the stock's closing price at the end of last week.
The Fresh Market has been working to grow its footprint and challenge high-end competitors like Whole Foods.
The deal is expected to close in the second quarter for 2016.
Private equity group Apollo has agreed to pay $1.3bn (£906m) for grocery chain The Fresh Market.