O'Keeffe is leaving the agency after 18 years to become WPP's worldwide creative director.
Gill joined BBH in 1998 and was promoted to the board in 1999. He has overseen creative on a number of the agency's accounts including Vodafone, Levi's, KFC, Boddingtons, Microsoft Xbox and Barnardo's.
He is currently creative director on the Vodafone global account and has written a number of supporting commercials including the launch film "mayfly", "work & play", "train", "time theft" and "cartwheel".
Gill is also creative director for Barnardo's and co-wrote the highly successful "believe in children" campaign.
In addition to Gill's promotion, Rosie Arnold has been named deputy creative director.
Arnold, who joined BBH in 1983, is responsible for the Lynx/Axe account, and also led the team that won the brand's digital account.
Simon Sherwood, chief executive of BBH Group, said: "This is an excellent opportunity for John. We are equally excited about our new creative leadership team of Nick Gill and Rosie Arnold, both great leaders and masters of their craft."