Former Australian captain Gregan demanded quality performances from the Wallabies as he led the nation to the 2003 World Cup final under Jones and the 58-year-old expects Farrell to perform likewise.
"Gregan was fantastic," Jones told reporters. "I have never seen a stronger winner than him. He demanded stuff from the team and they were frightened not to give it to him.
"That is close to the mark. Owen will put his own stamp on the team and we want him to do that. We obviously don't want him to lose some of the great work Dylan has done, but Owen can bring his own flavour."
Jones listed South Africa's John Smit and Japan's Michael Leitch as the best captains he had worked with alongside Gregan, and used them to highlight his point that Farell will need time to come into his own in the new role.
"You don't expect a captain immediately to be this all-conquering figure. It takes time, it takes effort and it takes patience," Jones added.
"...Owen has got the job for South Africa so he has five weeks to work through, find his own style, influence the team and we will see how he goes."
England, coming off the back of three successive Six Nations defeats, will play South Africa in Johannesburg (June 9), Bloemfontein (June 16) and Cape Town (June 23).
(Reporting by Aditi Prakash in Bengaluru; Editing by John O'Brien)
