The share sale is expected to value the Bolton company, previously called DRL Holdings, at around £1 billion, 14 years after it was started by kitchen appliances sales executive John Roberts, who owns a 40% stake.
Mr McBride will become the senior independent director at the company that claims a 24% share of the UK online market for major domestic appliances such as washing machines and refrigerators.
He has been chairman of online clothing retailer Asos since 2012, and is a director of the BBC as well as a senior adviser with venture capitalist Scottish Equity Partners.
He said he had been appointed to the role due to his skills in the areas of internet, digital, mobile and e-commerce as well as his long-standing board experience.
Mr McBride, a former director of Celtic Football Club, was managing director of Amazon.co.uk from January 2006 to September 2011.
Mr Roberts said: "AO has a strong track record of revenue growth and profitability and I am excited about the opportunities ahead as we continue to grow our new AO.com brand.
"A London listing will give us the platform to continue to grow our business. Ultimately, it is our ambition to be a leading European online electrical retailer."
The company, which rebranded its main site from Appliances Online to AO.com, wants to raise about £60m from issuing new shares while existing shareholders will also sell stock.