Lifelong Addicks fan Murray restructured the club during the summer when Charlton Athletic plc was effectively wound up over debts of more than £30m and made it known that they needed new investors.
Varney, who is also a long-standing Charlton supporter, was chief executive from 1997 until 2008 and he stayed on after that to help them find new investment.
The club statement added: "Baton 2010 Limited has accepted an indicative and legally binding offer for the acquisition of Baton 2010, Charlton Athletic Football Company Limited and Charlton Athletic Holdings Limited from an investor group represented by former Addicks chief executive Peter Varney."
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