Hornby left HBOS in February after it was taken over by the Lloyds Banking Group. He left the firm with more than £10bn of debts.
Hornby will take the role from from July 1 2009, and will report to executive chairman Stefano Pessina, who will continue to work full-time leading the group.
Alliance Boots is owned by US private equity firm KKR, and is Europe’s largest wholesale and retail seller in the pharmaceutical sector. It has 115,000 staff and reported a pre-tax profit of £13m in its 2008 end of year results.
Pessina says: “[Hornby’s] collaborative management approach aligns with our values, culture and team spirit.”