News Corporation is seeking to buy out minority investors in Fox Entertainment Group, its broadcasting subsidiary, for about $5.4bn (£3.7bn).
Fox's assets, including 20th Century Fox, are worth about $31bn
The media giant, run by Rupert Murdoch, owns 82% of the shares in the company, home to the Fox television network and the 20th Century Fox film studio.
The move follows News Corp's decision to register its business in the US.
20th Century Fox's recent film releases include I Heart Huckabees and I, Robot, while Fox puts out hit TV series 24.
Under the terms of the offer, minority Fox shareholders will receive 1.90 News Corp shares in return for each Fox share they hold.
Analysts said the decision to list News Corp in the US - which will result in the firm's shares trading in New York rather than Sydney- nullified the need to retain a separate stock market listing for Fox Entertainment shares.
News Corp investors voted in October to approve the transfer of the company's corporate domicile from Australia to the US state of Delaware.
The move is designed to help News Corp attract more investment from the largest US financial institutions, and make it easier to raise capital.
Fox Entertainment Group generated revenues of $12bn last year.
News Corp shares fell 25 cents to $17.65 after the share offer was announced while Fox shares were up 19 cents at $31.22.