Former Times editor Thomson, currently the paper's publisher, is expected to take on the top editorial role at the WSJ on an interim basis.
According to reports, he was already overseeing editorial matters for Dow Jones publications, including the WSJ, its newswires and Barron's magazine.
Brauchli departs the WSJ after just 11 months in the job, and only months after Rupert Murdoch's bought the paper, but is expected to remain within News Corporation.
Thomson joined Dow Jones from The Times in December, not long after the merger was completed. He was succeeded at The Times by James Harding. Before The Times, Thomson had been the editor of the US edition of the Financial Times for four years.
At the same time as Thomson was appointed publisher, Les Hinton, executive chairman of News International, publisher of The Sun and The Times, was appointed chief executive of Dow Jones, and Ian Weston, corporate development director of News International, was made senior vice-president of special projects.
News of Brauchli's departure comes just four months after News Corp's £5.6bn takeover of Dow Jones & Co, owner of the WSJ. Murdoch overcame fierce resistance from some quarters of the Bancroft family, who owned it, to win the takeover battle. One of his guarantees was that he would preserve the paper's editorial independence.
Brauchli worked his way up the corporate ladder at Dow Jones, from starting as a copyreader in 1984 to becoming the paper's managing editor almost a year ago.