The First Minister also revealed the line would open on 6 September 2015.
He said steam trains would operate from that month, and would be followed by a “significant expansion” when a visitor centre for the tapestry opens in the new Tweedbank station at the end of the line in 2016.
The 143-metre-long (480ft) artwork is the world’s longest embroidered tapestry, which tells the story of Scotland in 160 panels from the Battle of Bannockburn in 1314 to the reconvening of the Scottish Parliament in 1999.
Mr Salmond said a feasibility study led by Scottish Enterprise would examine how the 35-mile railway between Edinburgh and Tweedbank, south of Galashiels, could transform the region’s tourist potential.
A turntable for locomotives could be another possible visitor draw after the £350 million route opens after a gap of 46 years.
A new path will improve access to the Scottish Mining Museum from Newtongrange station.
The First Minister said: “For commuters and tourists alike, the re-opened line will provide opportunities to enjoy the many fantastic attractions and experiences on offer in the Borders.
“There will be few railway journeys anywhere in Europe to match the outstanding scenery along the route of the new Borders Railway.
“I have no doubt that the Borders Railway will be profoundly successful, and I will be one of the first in line for a ticket when the trains are running in September next year.”
Scottish Borders Council leader David Parker said: “Having the Great Tapestry of Scotland situated at the Tweedbank terminus telling the 420 million year history of Scotland is something that will be very special indeed.
“A great many people will take the ‘Train to the Tapestry’ and also visit the Borders and our many other attractions.”
Alistair Moffat, co-chairman of the Great Tapestry of Scotland trustees, said:
“It is very fitting and satisfying that a work of art that has been made all over Scotland, stitched by a thousand Scots, should come back home to the Borders, the place where Scotland’s textile industry saw its fullest flowering.”
Other measures include lengthening Galashiels station’s platform to accommodate longer tourist trains, following a similar move at Tweedbank after lobbying by campaigners.
Campaign for Borders Rail chairman Simon Walton said: “It’s gratifying so many recommendations made by the campaign are being actively discussed, although I would have hoped for some greater acknowledgement of our efforts, and recourse to our body of expertise.”
“I hope we’ll see the line established as a through route, carrying long distance trains between Edinburgh, the Borders, Carlisle and beyond.
“We would urge that the First Minister’s feasibility studies announcement be extended in scope to examine these benefits too.”
David Spaven, author of Waverley Route - the life, death and rebirth of the Borders Railway, said: “A key tourism issue which has still to be sorted out is how the charter trains will be accommodated within the limited single-track infrastructure being provided by Transport Scotland.
“With no spare ‘paths’ for charters over and above the half-hourly ScotRail service, other than in the evenings and on Sundays – and the length of double track cut back from 16 to 9½ miles – it will need a lot of ingenuity to properly accommodate tourist charter demand on the Borders Railway.”