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Mr Aue joined 2degrees in July last year and was previously chief financial officer at Vodafone New Zealand. He had also worked for Vodafone in Britain and Fiji.
Chairman Brad Horwitz said Mr Aue's appointment followed an international search "that attracted a high calibre of applicants".
"Mark has impressed the board with his financial management, active leadership and understanding of our business today and the opportunities ahead," Mr Horwitz said in a statement.
"Coupled with his extensive local and global industry experience, we are delighted to make an appointment that will ensure stability and continued growth at 2degrees."
2degrees is New Zealand's third-largest mobile provider after Vodafone and Spark. It had about 24% of the market in 2017, the Commerce Commission said in August.
Mr Sherriff had chaired 2degrees since 2010 and stepped into the breach in April 2013, after former chief executive Eric Hertz was killed in a light plane crash
off the west coast of Waikato.
Mr Aue said leading 2degrees was a unique opportunity and something he had long aspired to do.
"Few companies have made as much impact on the everyday lives of kiwis as 2degrees," he said, adding that he had been watching the company from afar before joining it.
"Since joining the team, I've been impressed by the passionate culture, the strength of our people and how dearly the brand is regarded by customers."
2degrees is approaching its 10th birthday.