He resigned as chief executive in 2013 after suffering ill health and denies the allegations against him.
Mr Johnson wrote: “We have commissioned an independent law firm and are appointing an independent accountancy firm to advise the JLC.
“We want to ensure no stone is left unturned in understanding past events and that there is as much visibility as possible.”
As part of the review Mr Newmark will be invited to participate.
Mr Johnson said the JLC was now a very different organisation, “operationally and otherwise”.
“It not only has a new chief executive, but also a new chairman, Jonathan Goldstein – a former lawyer like myself – seven new trustees, and a new strategic direction.”
He added that the review, however “painful” for the organisation, would be an opportunity to demonstrate that the “JLC is fully committed to being transparent, accountable, and a home of best practice”.
Jo Coleman, a partner at Womble Bond Dickinson and an expert in charity law, will provide the legal advice. The costs of Ms Coleman's work, and that of the accountancy firm, will be covered by the JLC.
