Penn will replace David Thodey, who has led the company for almost six years and is now retiring.
“Andy is a seasoned executive in global markets with proven capability to lead organisations through significant transitions and major expansion,” said Catherine Livingstone, Telstra chairman.
“It is testament to David Thodey that we were able to select the next chief executive from within the business.”
Bray is Telstra’s existing group managing director of products, and his appointment is also effective May 1.
Since joining the company in 2009 as head of corporate strategy, Bray has worked with Thodey to redefine Telstra’s corporate growth strategy and reiterate its emphasis on customer service.
In his role as GMD of products, Bray has been responsible for approximately $15 billion in annual revenue including mobile, cable, ADSL, PSTN, NBN and Wifi.
“Warwick has decades of knowledge in and around telecommunications and technology and significant financial experience proven by his business results in Telstra and other companies,” Penn said.
“He is well regarded in the industry and has a proven track record in leading and significantly growing multi-billion dollar businesses.”
In Februrary, Telstra also appointed Erez Yarkoni as its chief information officer.