Thomson is on secondment from the Australian Rugby Union, where he is the national body's integrity manager.
"We're delighted to be able to appoint Phil to the acting role," Brumbies Chairman Rob Kennedy said in a statement on Thursday. "He has an impeccable reputation in the game locally, nationally and internationally.
"He is a safe pair of hands and exactly what we need given the recent turbulence in our organisation."
Jones was stood down by the Canberra-based side in March following a controversial radio interview in which he spoke about a report into the club's finances but stayed in the job with protection from whistleblower laws.
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He then stepped down last month after reaching a confidential agreement with the club, who said at the time it would allow both parties to avoid a lengthy court battle.
Thomson, who worked for the Australian Federal Police for 14 years, was the Brumbies team manager from 1996 until 2001 before he became the manager of the Wallabies. He stayed in that role until 2010.
"My appointment is an interim measure to enable the Brumbies organisation to move forward and finish the season with confidence and enable a thorough recruitment process for a new CEO to take place," Thomson said.
"I am looking forward to this opportunity."
The Brumbies top the Australian conference in the Super Rugby standings on 25 points, but have played one more game than the New South Wales Waratahs, who also sit on 25 points.
The Brumbies play the Rebels in Melbourne on Friday.
(Reporting by Greg Stutchbury in Wellington; Editing by Peter Rutherford)
