VisitScotland will follow it up with promotional activity in Germany early next year.
It said the route - officially opened by the Queen last week - had received coverage by media worldwide.
It hopes it can "breathe new life" into the economies of Midlothian and the Borders and help Scotland as a whole.
Mike Cantlay, who chairs VisitScotland, said the start of services was "not only a historic moment for Scotland" but also "a truly global affair" with an audience of millions.
"The magical Scottish Borders is one of Scottish tourism's greatest assets with its rich heritage and beautiful and inspiring landscape," he said.
"The Borders Railway, which delves deep into Sir Walter Scott country, presents a huge opportunity for Scottish tourism to breathe new life into the area, touching on every industry, business and community."
Infrastructure Secretary Keith Brown said the railway would "open up a unique and iconic part of the country to visitors".
"Having been there myself at the official opening on Wednesday to sample the atmosphere and feel-good factor I have no doubt that the new line will serve as a catalyst for major investment in the area," he said.
"Not only is the Borders Railway a success by the scale of its ambition, but also for bringing together communities, councils, and government to deliver a challenging infrastructure project both on time and on budget.
"Such vision and collaboration means that the Borders has become a symbol of the renaissance of our railways in Scotland."
Danny Cusick, who chairs the Borders Railway Blueprint Leaders Group, said it hoped to "maximise the economic benefits" of the new rail connection between Edinburgh and Tweedbank.
A ScotRail Alliance spokesperson added: "There's a great buzz about the Borders Railway, particularly after such a successful opening weekend, with more than 2,500 journeys last Sunday alone - the first day of passenger rail services to and from Tweedbank.
"We're pleased to be working with Scottish Rail Preservation Society to run our first-ever steam trains.
"These are proving popular with customers and helping boost the Borders economy.
"Due to the huge demand, we added extra carriages to 16 of our 17 Borders steam trains, with these additional tickets selling out within a week."
Tourism chiefs are planning a marketing campaign in America as they look to exploit the "great buzz" created by the new Borders to Edinburgh railway.