Fiamma has been head of the Cleveland-based firm's City practice for 10 years and has overseen its expansion into one of the largest US offices in London.
He will join A&O as an equity partner in the tax department.
Fiamma says one of the reasons for his departure is that he was weary of combining management of the office with his own practice.
“The administrative burden was taking me away from seeing my kids grow up,” he says.
“When I got the approach from Allen & Overy – and it was an approach – I wasn't looking to leave, but it seemed to make sense. I knew them and felt very comfortable with them.
“I have made my career here in London and, although I am not English, I am here for good and I think I would enjoy being with a firm that sees this as its home.”
Litigation partner Robert Thomson takes over as head of Jones Day's London office. Thomson joined the firm from Denton Hall, where he was head of the Hong Kong office for four years.
Thomson says: “I have been in the firm for just over three years, but I worked with it for many years before that and I know a lot of people in the US and throughout the firm.”
Former Linklaters partner Keith Featherstone takes over as head of the London tax practice.
A&O's head of tax Patrick Mears says: “We are delighted to be joined by someone with Stephen's reputation and profile. He will strengthen our ability to provide a cross-border tax service while enhancing our US law practice.”