Mr Horta-Osorio temporarily left the firm on 2 November on a leave of absence for health reasons.
He is expected to return by the end of the year but if not, the group has appointed David Roberts as its interim chief executive.
Tim Tookey is currently serving as acting chief executive but he will be leaving in February for a new position with Friends Life.
Mr Roberts has been a non-executive director with Lloyds since March 2010 and is chairman of the Risk Committee.
He was previously chief executive of international retail and commercial banking at Barclays.
Sir Win Bischoff, chairman of Lloyds Banking Group, said: “David Roberts has impressed his colleagues on the Board and the Group’s senior management with his understanding and broad experience of the banking and financial services sector. He has a strong track record in retail and commercial banking at the highest level.”
The Group also announced that Nathan Bostock would be remaining at Royal Bank of Scotland rather than joining the Group to help with restructuring the wholesale business.
Mr Bostock works as head of restructuring and risk at RBS.
As a result, Truett Tate will be remaining in his role at the Group as group executive director of wholesale.