He will report to Rebekah Brooks, chief executive of News UK. The publisher of The Sun and The Times acquired Wireless in September.
Wireless owns radio stations including Virgin Radio, which relaunched in March, and talkSPORT.
Taunton replaces John McCann who retired after 16 years in the role, and 23 years at the company, when the business was known as UTV. Wireless was formed when UTV sold its television business to ITV.
Richard Huntingford, the executive chairman at Wireless, stepped down in September. Huntingford joined the company as chief executive of UTV Media in 2012 and was previously chief executive of Chrysalis for seven years. He was made executive chairman in March following the News UK takeover.
Brooks said: "Scott is a dynamic leader, whose promotion to the role of chief executive will be a huge asset to Wireless and News UK.
"He will join my executive team and work to ensure that our two businesses build on the strengths of a partnership that is already demonstrating great success in editorial and commercial collaboration."