Hornbrook will be replaced by chairman Stuart Bernau, who will combine the roles of chief executive and chairman while a longer term replacement is found. Bernau was only appointed as chairman last month.
Hornbrook has worked for Chelsea Building Society for the past 28 years, with the last four as chief executive.
In March Chelsea building society revealed losses of nearly £30m due in part to a £55m exposure to two Icelandic banks.
A provision of £44.3m was set aside against the potential loss, but Chelsea was also hit by a £10.2m FSCS levy and the write-off of goodwill of £15.4m arising on the acquisition of BCS Loans and Mortgages.
Bernau says: “Richard Hornbrook has played an important role at Chelsea over the last 28 years. During this time, he has instilled values into Chelsea that have created an engaged workforce that is committed to offering a great customer experience to our members. These values have served Chelsea well and I am committed to maintaining them.”