Bruce, 54, will step into the fray of the weekly political debate programme, known for its lively exchanges between politicians and the public.
The ‘News at Ten’ presenter’s first ‘Question Time’ will be on Thursday 10 January 2019.
Dimbleby, 80, announced in June that he would step down from the programme after 25 years this month.
Bruce said of her appointment on Friday: “It is an honour to be asked to take on one of the great political programmes of the BBC. Particularly at a time of such historic change for the UK and tumult at Westminster.
“For many years ‘Question Time’ has been presented by one of my television heroes so I am thrilled and not a little daunted to be stepping into his shoes. But it is a programme I have watched for as long as I can remember and have long wanted to be part of. I can’t wait to get started.”
The selection process for the role saw candidates host pilot episodes of the programme, including panellists and a live audience.
Fran Unsworth, the director of BBC News, said: “David is a tough act to follow, but Fiona impressed us all – with her authority, warmth, and ability to connect with the audience and champion their concerns. We’re delighted to have her at the helm.”
Bruce, who has worked at the BBC since beginning her career as a trainee in 1990, has helmed the corporation’s main news bulletins since 1999, as well as Sunday favourite ‘Antiques Roadshow’.