SABMiller bought Meantime, a London-based craft brewer, last May and until now Meantime was headed by chief executive Nick Miller.
SABMiller is in the process of selling Meantime, Peroni and Grolsch to Japanese brewer Asahi, to meet regulatory requirements governing its own acquisition by the world's biggest beer company, AB InBev.
Edwards will succeed Miller on 31 March. She has been in her current role for a year and a half and has also had spells in marketing at Anheuser-Busch and Pernod Ricard.
It is not clear how she will be replaced at Peroni, with SABMiller unavailable for comment.
Edwards said: "Meantime Brewing Company has enjoyed outstanding growth since its launch in 2000 and in that time Nick and the team have taken beer production to new heights, turning Meantime into Britain’s leading craft brewer.
"I have long been a huge fan of the brand so this appointment is a huge honour for me and I am looking forward to working with the team in Greenwich to continue building on the success of Meantime in the UK and beyond."