April 24 (Reuters) - U.S. food and grain-handling companies ConAgra Foods Inc, Cargill Inc and CHS Inc have moved closer to sealing a deal to merge their North American flour mill operations by agreeing to sell four mills to a Japanese company.

Miller Milling Co, a U.S.-based unit of Tokyo-based Nisshin Flour Milling Inc, will buy the four U.S. mills, the companies said on Thursday.

Divesting the operations was part of the companies' plans to complete the merger and create a company called Ardent Mills, which would control a third of the U.S. flour market.

Completion of the deal has taken longer than expected due to an investigation by the U.S. Justice Department's antitrust division.

Under the deal, ConAgra is joining forces with Horizon Milling LLC - a joint operation between Cargill and CHS that already is the largest flour miller in the United States. The deal was first made public in March 2013 and was initially expected to close late last year.

Those flour mills are Horizon's facility in Los Angeles and ConAgra's facilities in Oakland, California; Saginaw, Texas; and New Prague, Minnesota.

(Reporting by Josephine Mason; Editing by Lisa Von Ahn)