Mills' hire follows a four-month interim stint at the company. She was previously global head of media practice at the Anglo-Australian mining firm Rio Tinto, where she worked largely in emerging markets such as China, India and more.
In her role, Mills has replaced Nigel Fairbrass, senior vice-president of global comms and reputation, who left the group in February.
She will report to Catherine May, group corporate affairs director, who said: "Christina has a very strong track record as a corporate communicator and came highly recommended for her work at Rio Tinto.
"She hit the ground running in February and I am really pleased to appoint her to the role permanently."
Mills said: "In my first few months here we have launched a new corporate website, new brand visual identity and high-profile sustainable development ambition. I’m really looking forward to helping shape communications strategy further."
SABMiller brews Peroni and Pilsner Urquell among several beer brands.