Sir Dennis, 53, takes over the post at the end of July when Jon Foulds, the former 3i chief executive who steered the Halifax to flotation, retires at the age of 67.
Mr Foulds, who has known Sir Dennis for years, first approached him about the position last year. He said that the Halifax was fortunate to have found someone of Sir Dennis's calibre to take on the role.
"He is pretty well-known as a strategic thinker. But also a doer. I don't need to wish him luck because he is the kind of person who will make his own luck," he said.
Apart from a much-needed holiday, Mr Foulds says that he has no firm plans about what to do with his new-found free time.
Sir Dennis, whose high-flying career has straddled both the public and private sectors and the arts, said he has a high regard for Jim Crosby, the Halifax chief executive whom he knows from the time when both were on the board of J Rothschild Assurance.
Recently, Sir Dennis stepped down as chairman of the Trustees of the Tate Gallery. He has promised to cut down on his "non-core" activities to give him more time to devote to his new role.