O'Keeffe, who has been at BBH for 18 years, is still in negotiations with WPP and a start date is yet to be confirmed.
He said: "Most people presumed I was a BBH lifer, it's a hell of a place and I've had a great time. But WPP invited me to have a chat, I thought about it, and decided it's just the type of role that you can't turn down."
O'Keeffe joined BBH in 1990 and was made executive creative director in 2000.