The deal is for the original $5 billion price that Murdoch had offered and will be put to the full Dow Jones board Tuesday for its approval, the Journal said, citing unnamed people familiar with the situation.
The deal would still need approval from Dow Jones' controlling shareholders, the Bancroft family, which has been divided on a sale to News Corp. because of concerns over whether the Journal would maintain its editorial independence.
Michael B. Elefante, the Bancroft family's lead trustee, has scheduled a meeting for Thursday to present the agreement to the family and is expected to give the family members several days to make a decision, the Journal reported.
Representatives of Dow Jones and News Corp. did not immediately return telephone messages seeking comment.
Negotiators from the two companies reached the agreement in principle Monday, the Journal said.
Murdoch, News Corp.'s chairman, resisted pressure from Dow Jones to raise his initial $60 a share offer, which represented a premium of about 65 percent over the mid-$30s level that Dow Jones stock was trading at before the proposal became public in early May.
Dow Jones shares fell 54 cents to $56.95 Monday.
The Bancrofts originally rebuffed Murdoch's approach but then reversed themselves and agreed to meet with him in early June to discuss their concerns about keeping the Journal's coverage free from corporate interference. The talks led to an agreement that would create a committee that would have to approve the hiring or firing of top editors at the Journal.
Murdoch has long wanted to own the Journal, which has tremendous clout in the business world and wins many prizes for editorial excellence. Murdoch has said he would invest in the Journal's online and overseas operations, and tap its resources to help build a business-themed cable news channel that would rival General Electric Co.'s highly profitable CNBC network.
Besides the Journal, Dow Jones also owns Dow Jones Newswires, the Factiva news database, Barron's, a group of community newspapers and several well-known stock market indicators including the Dow Jones industrial average.
News Corp. owns the FOX broadcast network, FOX News Channel, newspapers in the United Kingdom, Murdoch's native Australia and the New York Post, the Twentieth Century FOX movie and TV studio and MySpace, the online social hangout site.
The Bancroft family has controlled Dow Jones for more than a century through a separate class of stock that grants increased voting rights. Other newspaper publishers including The New York Times Co. and The Washington Post Co. have similar arrangements that allow families to retain control.
News Corp. is the parent company of FOXNews.com.