The Portuguese 52-year-old has written to staff following reports that he took a mistress with him on a business trip to Singapore when he ran up a £4,000 hotel bill.
Shareholders in the group, which includes Bank of Scotland and Halifax, asked questions about his future when the affair emerged.
The bank declared that the £8.5m-a-year salaried CEO, who is married with three children, did not breach company guidelines as his expenses were met from his own resources.
In his note to 75,000 employees he said: “Having returned to work I wanted to use the opportunity to address the recent media coverage of my private life.
“As you may have read, my expenses were reviewed in light of speculation by certain newspapers and the Group has confirmed that they are fully compliant. As you’d expect, I pay for my personal expenses whilst away and only reclaim what is a business expense.
“My personal life is obviously a private matter as it is for anyone else. But I deeply regret being the cause of so much adverse publicity and the damage that has been done to the group’s reputation.
“It has detracted from the great work which you do for our customers on a daily basis and from the major accomplishments of the past five years.
“This includes the Government shareholding having reduced from over 40% to around 9% with over £16 billion plus dividends having been returned to taxpayers.
“More broadly I have been a strong advocate of expecting the highest professional standards from everyone at the bank, and that includes me.
“I will continue to strive to meet those standards. Having the highest professional standards raises the bar against which we are judged and as I have always said we must recognise that mistakes will be made. I don’t expect anyone to get everything right all the time.
“The important point being how we learn from those mistakes and the decisions and actions we take afterward.
“As we look forward, it is your hard work over the last five years returning the Group to financial health that means we are best placed among our peers to continue supporting the UK economy and to help Britain prosper.
“We chose to focus on helping the UK economy – in particular through our support for first time buyers, small businesses and UK corporates – and as a result by choice, our future is inextricably linked with the future success of the UK economy.
“The extended period of low interest rates that we now face has created uncertainties for the UK economy and new challenges for the Group.
“And as a UK focused bank we are not immune to the factors likely to shape the UK economic outlook, but I believe we will be well positioned to meet them.
“With that in mind please be assured that I am as committed as ever to leading the Group forward to deliver our strategy and to meet our future ambitions. Thank you again for your messages of support over the last few weeks. I have greatly appreciated them.”
Mr Horta-Osorio who has been married for 25 years to Ana, was pictured with Dr Wendy Piatt, a former adviser to Tony Blair and an education expert who is said to bear a resemblance to his wife.
He became chief executive of Lloyds in March 2011 after leaving Santander UK. A few months into the role he took extended sick leave because of a stress-related illness.
He has since been credited with a major turnaround which has seen the bank return to profit and the dividend list and almost wholly back in private hands.