Eventually, enough of them agreed to accept $60 a share for the company - a 65 per cent premium over the value of Dow Jones shares -immediately before the bid became public.
Analysts and Dow Jones employees have questioned whether The Wall Street Journal's quality and independence will suffer under Murdoch who is also a tabloid newspaper owner and head of one of the most conservative cable news outlets in the US, Fox News.
Tuna Amobi, a senior media analyst with Standard and Poor's, said it remained to be seen "whether this is going to actually ensure continued editorial independence".
Murdoch, who owns a large portfolio of newspapers, magazines and television stations around the world, conceded that there was "nervousness" among the Dow Jones staff over his takeover.
But he added that it had "died down" and he has agreed to set up an editorial oversight board to allay fears.
On Thursday, he addressed several hundred Wall Street Journal reporters in the paper's main newsroom.
"Our aim is pretty simple. We have to entertain, inform, enrich all our readers in their lives and in their businesses. We must be the pre-eminent source of financial information and comment in the world," he said.
"We want to globalise it and digitise it. There is a lot to do."
Murdoch has already begun the process of reshaping management at the paper, announcing two appointments last week: Robert Thomson, editor of British paper The Times, to be publisher of The Wall Street Journal and Dow Jones; and Les Hinton, executive chairman of News International, Murdoch's British newspaper group, to be chief executive at Dow Jones.