The move follows the decision of current chief executive Hugh Burkitt to step down after 13 years.
The changes, which form part of the society’s global expansion strategy and a wider restructure, will take effect from 1 January 2017.
In a statement, the organisation said Burkitt would remain "an integral part of the society taking up the newly created position of global ambassador". It added that he would "work alongside Gemma helping to deliver the company’s five year global strategy as well as seeking out new opportunities and promoting the society internationally".
Reflecting on the changes, Burkitt said: "Being CEO of the Marketing Society has been a great privilege and the past 13 years have flashed by, but after nearly a decade of working in partnership with Gemma, I think it is time to let her take full control of the global expansion that she has led so effectively.
"I will continue to work for the Society with the specific task of developing our Excellence Awards internationally."
In her new role, Greaves will continue focusing on the Society’s vision to become the leading global network for senior marketers, raising the profile of marketing within business and delivering on their purpose – to inspire bolder marketing leadership.
Greaves said: "It’s been such an honour to work with Hugh over the past 10 years. His wisdom, depth of knowledge and sharp wit have constantly inspired me.
"He’s been an incredible leader and I’ve learned so much from him. His are huge shoes to fill, but I’m really excited about the opportunities ahead as we work towards our global ambition of having 10 global hubs by 2020."
Stephen Maher, the chairman of the society, and the chief executive at MBA, described Greaves as having "phenomenal energy, charm, commercial prowess and global vision".
Maher said: "She embodies the Society’s mantra of ‘inspiring bolder marketing leadership’ and we are very lucky she has agreed to take on this role and sprinkle more of her magic on the Society and the industry at large in these exciting years ahead."