The files of both lawyers were seized through search warrants.
Prosecutors had asked Manhattan federal Judge J. Paul Oetken on Thursday to appoint Jones as special master, and in a court filing told the judge that attorneys for Giuliani and Toensing supported that request.
"Judge Jones's reputation for integrity and fairness made her the unanimous choice for all parties," Giuliani's lawyer, Arthur Aidala, told CNBC. "We look forward to working with her."
Cohen, in a text message to CNBC, said, "Judge Jones was professional in the review and determination of attorney/client privilege of the more than 10 million documents in my case."