His appointment is significant for CNBC - during his time at Turner, Buckley was responsible for advertising sales and distribution for all of the company's properties, including the rival news channel CNN.
Buckley, 39, took a sabbatical from Turner 15 months ago to complete a Harvard management course. In his new role, he will oversee all commercial aspects of CNBC's business.
Miller, who had the title of executive vice-president, sales and marketing, is returning to the US to take on a position with the CNBC group.
Buckley said: "It is an extremely important time to be joining CNBC Europe. It is an exclusive product with a highly valuable audience. My role is to build on the channel's commercial strategy, helping to identify new opportunities to maximise both ad sales and subscription levels, and take the channel to a new level in terms of its client focus and approach to new-business development."