PRWeek reported in April that the account was out to pitch, with the company looking for one or two UK agencies with a global network. Brunswick was understood to have repitched for the work.
The agency review followed the arrival of corporate affairs director Alex Cole, who joined Bupa last year from Sainsbury's.
Stephen Bethel, director of external relations at Bupa, said: "As we look to strengthen our leading market positions across the globe and build our profile, we want to ensure that we continue to tell our story effectively. We were impressed with FTI’s specialist sector knowledge across both the insurance and healthcare sectors, combined with its global perspective."
Deborah Scott of FTI Consulting said: "We are delighted to have been chosen as Bupa’s financial communications adviser. It is an organisation with a strong purpose and clear vision for the future and we’re looking forward to helping the company realise its ambitions and further cement its reputation."
Bupa funds and provides healthcare for 29 million people in 190 countries. The company was in the news earlier this month over plans to sell off 200 UK care homes.