Mills had been with Constellation for 16 years, and was recently promoted from managing director of the Gaymer Cider Company to man the global giant's European sales operation.
He told OLN: "Taking total responsibility for running a drinks company is something I really wanted to do. While I'm enjoying what I'm doing here, ICB are a great bunch of guys Ė innovative, creative, and I just like the culture of what they are trying to do. It is about the same size as this company was when I joined it."
He added that he is looking forward to launching new brands and developing the supplier's existing products in the UK and possibly abroad.
ICB was founded in 1990 by John Hibberd and Paul Burton, and its brands include Vodkat, St Helier cider, The Italian Job wine and Zamaretto.
Burton said: "This is a major appointment and very much in line with our strategy and vision for the company. John is a senior figure in the industry. He has just the energy, high level expertise, leadership qualities and focus that will most assist us in driving our business on to the next level."