In a joint bid, Metropoulos & Co and Apollo Global Management are paying $410m (Â£275m) for the bankrupt company.
The offer had originally been planned to set the floor for an auction, which Hostess boss Greg Rayburn had predicted would be "wild and woolly".
In fact, a court filing showed that no other offers were submitted.
The deal, which also includes Suzy Q's and Cup Cakes,  is expected to be approved by a bankruptcy court on 19 March.
Hostess Brands started winding down its companies last year, after being hit by rising food prices and a bakery strike.
An auction for Hostess's bread brand, Wonder, has also been cancelled, with a view to selling it directly to Flowers Foods, which makes Tastykakes and Nature's Own bread.
Hostess Brands is selling its cake bakery business, which includes Twinkies cakes, to two private equity companies.