News Corporation, whose newspapers include the Times and the Sun, agreed the takeover with Dow Jones's controlling Bancroft family.
Mr Murdoch said he would be "an equally strong custodian" of the business, which will join Fox News, the Twentieth Century Fox film studios, and social networking website My Space in the News Corp stable.
Bancroft family members and trustees representing 37 per cent of shareholder votes agreed to support the deal. Public shareholders holding 29 per cent of votes are also likely to back Mr Murdoch's bid.
There have been concerns over the future editorial independence of the Wall Street Journal under News Corp's ownership.
But the two parties have agreed to establish a five-member committee to ensure the "continued journalistic and editorial integrity" of Dow Jones's publications and products.
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