Bowe will take over from Lord David Currie, the regulator's chairman since Ofcom's inception in 2003.
The Government has invited the Business and Culture, Media and Sport Select committees to approve the appointment of Bowe, which is expected to take place in January next year.
Andy Burnham, culture secretary, said: "Colette has the right mix of skills and experience for this role and I'm confident she also has the vision necessary to take Ofcom forward and tackle its future challenges."
Bowe, a 61-year-old trained accountant, started her career as an economist at the Department of Trade and Industry after which she worked at the Independent Broadcasting Authority. She has also served as the chief executive of the Personal Investment Authority and as executive chairman of the Fleming Funds Management.
She currently holds a number of board membership roles including sitting on the boards of Axa Framlington, and Morgan Stanley Bank International.
Business secretary Peter Mandelson, said: "The communications industries have huge significance for our economy during these challenging times, and Colette's knowledge and experience across business, regulation and Whitehall will be invaluable at Ofcom in helping deliver greater choice and innovation across the sector."