The announcement followed the release of a report by an influential Wall Street analyst suggesting Viacom should consider such a move in a bid to boost the company's share price.
For months the idea has been floated within Viacom by its two co-chiefs Tom Freston and Les Moonves, according to a source.
Initially, Redstone had been skeptical, but in a statement Wednesday the controlling shareholder said such a deal could be a boon to shareholders.
"It is clear that, despite our success in operating our businesses for maximum return, Viacom's businesses have inherently different growth characteristics and investment attributes that appeal to different types of investors," Redstone said in a statement.
"Furthermore, it has become clear that this important distinction is likely to continue to limit Viacom's ability to receive full value for its assets and its prospects in the investment community."
Redstone promised to announce further details in the second quarter.
In a research report issued Wednesday, Merrill Lynch media analyst Jessica Reif Cohen noted that Viacom's stock has languished, saying, "If [the] market fails to recognize [the] value of [the] assets, breaking up the company should be considered."
Viacom's stock has been held down by the company's slow-growth businesses such as radio and outdoor advertising. Breaking up the company could unlock value from the company's high-growth movie and television businesses, Reif Cohen wrote in the report.
Viacom said the company could separate its MTV Networks (search) and Paramount movie studio into one company run by Freston, with Moonves running the CBS network, its affiliates and Paramount Television (search).
"In addition to unlocking the value of the individual assets, breaking up the company could solve the management succession issue," Reif Cohen wrote.
Last summer, Viacom president Mel Karmazin (search) resigned and Redstone installed Freston and Moonves as co-presidents and co-chief operating officers. Both are competing to succeed Redstone, who is expected to step down in a little over two years.
In yesterday's statement, Redstone said: "The transaction would further the logical and orderly succession process that we put in place and would allow Viacom and its shareholders to take full advantage of the skills and experience of our deep management."