Hornby, who was chief executive of HBOS in 2008 when the bank nearly collapsed under the weight of £11bn losses, says he wants to spend a few months away from the corporate world after “an intense last five years”.
He left the bank soon after it merged with Lloyds TSB.
Alliance, which owns the Boots brand in the UK, says it will launch the search for his successor “in due course”.
It adds that it “continues to perform well” and will report “strong trading” when it announces its results for the year ended 31 March in May. In the year to 31 March 2010, profit increased to £602m, while sales rose to £22.5bn.
Alliance Boots was created by the merger of Boots the chemist and Alliance Unichem in 2006. It was subsequently bought by private equity firm KKR in 2007 in a deal believed to be worth £11bn.
Former Asda executive Hornby joined Alliance Boots in June 2009. He will leave Alliance and its board with “immediate effect”.