Both men were selected in the Lions squad for their summer tour of Australia, with the Welshmen revealed as the side's skipper by head coach Warren Gatland.
The Ireland international believes that Warburton will be a success as the party's leader.
"He has done a very good job as it is," O'Connell told Sky Sports News. "He just needs to continue to be himself and doing it the way that has been so successful for Wales.
"There is no need to change. He has been picked for who he is and what he has been doing. That's the only bit of advice I have for him but I am sure he is well capable without my advice."
O'Connell also believes that he is lucky to have been selected for the tour.