The decision follows his meeting with the Nabs president, John Bartle, who will take on Lace's responsibilities until a replacement is found.
Lace claimed that his heavy commitments at Grey, currently undergoing a major overhaul, and at the IPA prevented him from giving enough time to the job and sufficient support to the Nabs chief executive, Kate Harris.
"Over the past three months, we've agreed it would be in everybody's interests if Nabs found somebody who had a lot more time for the job than I've got," he said.
Lace agreed to take on the Nabs role when he was still the chief executive of TBWA\ London and before he had committed himself to Grey.
Since then he has been carrying out a restructure of Grey London.
He is also a member of the IPA council and the chairman of its training and development committee, which has been responsible for putting together the IPA's qualifications programme.
During Lace's chairmanship, Nabs has been rethinking its fundraising activities. This includes the scrapping of its annual boxing night, which provides the bulk of its annual income, and its replacement by a new event early next year.
Bartle said: "Everybody at Nabs is grateful for everything Garry has done in the middle of a heavy workload."