Thomas L. Williams and William J. Williams Jr., president and chairman, respectively, of Cincinnati-based North American Properties, are the other members of the purchasing group.
Under terms of the deal, Castellini would replace Carl H. Lindner as the team's CEO.
"Carl has meant so much to the Reds and the city of Cincinnati," Castellini said in a news release. "As such, we are thrilled that he has agreed to continue his association with the club as a significant partner in our ownership group. I look forward to finalizing the agreement and submitting our group for MLB approval in the very near future as we are very excited about this opportunity and are eager to get started on the work ahead."
Several existing owners, including Lindner, George L. Strike and William J. Reik Jr., are expected to retain an interest in the team, according to the release.
Great American Insurance Company and a subsidiary of Gannett Co., Inc., are expected to sell all their interests.
Shares of the team totaling about 51.5 percent went up for sale in early March by minority owners Louise Nippert, Strike and Gannett.
Lindner, however, was originally expected to retain his controlling interest in the team. He did not release a statement on his decision to give up that control and did not immediately return calls seeking comment.
"In selecting the Castellini group, the commitment of Bob Castellini and Tom and Joe Williams to our community was a very important factor to all of us," Strike said in the release.
Because the Reds have not had a winning season since 2000, the news of the sale is likely to leave many fans hoping a change in ownership will result in a change in fortune on the field.
The purchase price of the interests sold will be based on an enterprise value of the club of approximately $270 million.
Before the deal can be finalized, it must first be approved by the other Major League owners. The next quarterly meeting of the owners doesn't take place until January, though a special vote could potentially take place before then.
The parties expect to complete the transaction before the end of the year, according to the release.
Castellini and the Williams brothers both have previous connections to baseball.
Castellini, whose company is a wholesaler of fruit and vegetables, is part of the St. Louis Cardinals' ownership group headed by Cincinnatian Bill DeWitt. The two men previously invested in the Baltimore Orioles.
The Williams brothers' father and uncle were major owners of the Reds from 1966-84.
Until the necessary approvals are granted, Castellini and the Williams brothers are precluded from making comments on the deal.