Members of the public were invited to submit suggestions for the name of the new five-floor health centre, which is being built on the corner of Trafford Way and St Sepulchre Gate in the town centre.
Those suggestions were then whittled down to a shortlist and the final name was decided upon by a panel of judges.
The name of The Flying Scotsman Centre was the suggestion of Pamela Crich from Earlsemere Avenue in Balby, who has won 50 in gift vouchers for her contribution.
In her entry, Mrs Crich said of the health centre: "It will have a fast, efficient service and streamlined design similar to its counterpart the Flying Scotsman steam engine."
Roger Greenwood, chairman of NHS Doncaster, said: "This is a landmark building in the heart of Doncaster and this is a fitting name that celebrates the history of Doncaster.
"It is fantastic that a local resident has given the centre a name that has huge significance for the town and is something that we can all be proud of.
"We are planning to display artwork, drawn by local people, within the centre that reflect its momentous name."
When it opens in autumn next year the new centre will provide a range of health services from 8am to 8pm every day of the year.
It will also have a range of environmentally-friendly features on the building such as solar panels and a system for collecting rainwater.