The appointment of Mr O'Sullivan reignited speculation that BAT is seriously considering a demerger of its financial services activities, which include Allied Dunbar and Threadneedle Asset Management, from its litigation-prone tobacco core.
Sandy Leitch, chief executive of British American Financial Services (BAFS), denied any connection between the move to strengthen Eagle Star's management and any demerger plans.
"If you intend to be the best, you have to recruit the best and that's exactly what we've done," he said.
Mr Leitch added: "I am absolutely delighted to have recruited such an outstanding individual as Patrick to this key position.
"The appointment reinforces our commitment to develop the whole of BAFS into the UK's leading insurance and asset management group."
Mr O'Sullivan's departure is a blow to BZW, which has suffered several high-profile departures in the run up to its move this year to new offices at Canary Wharf in London's Docklands.
Like NatWest Markets, BZW is working hard to justify its position to shareholders in Barclays, its parent, who are growing increasingly impatient with the low returns from investment banking.
Prior to working for BZW, Mr O'Sullivan gained experience of the insurance business as general manager of GE's Financial Guaranty Insurance Company. He is expected to take up his new job in September.
The possibility of a demerger of BAT's insurance and asset management businesses gained credibility in April when Lord Cairns, chairman, said there were "no sacred cows" and declared an open mind on splitting the group up.