Alex Salmond has announced that the first services will begin on the Tweedbank to Edinburgh line on September 6, 2015. Passengers will be able to travel end to end in around 55 minutes.
The £294 million project has seen the construction of 30 miles of new passenger railway and seven new train stations - four in Midlothian and three in the Scottish Borders.
All seven stations will be equipped with wifi and the platform at Galashiels station will accommodate longer tourist trains. There will also be a new footpath at Newtongrange Station to enable direct access for users of regular rail services to the award-winning Scottish Mining Museum.
The First Minister also unveiled a feasibility study which will examine how to capitalise on the new Borders railway to boost tourism in the region. The study will be led by Scottish Enterprise in partnership with VisitScotland, Scottish Borders Council and Transport Scotland.
The study will also look at tourist opportunities from any future development of the line, including the potential for a train turntable and the creation of a permanent home at Tweedbank station for the Great Tapestry of Scotland, the world's longest embroidered tapestry, reflecting the textile heritage of the area.
Mr Salmond said: "From September 2015 - for the first time in almost half a century - there will be passenger train services running on this track.
"For commuters and tourists alike, the reopened line will provide opportunities to enjoy the many fantastic attractions and experiences on offer in the Borders.
"We can expect the Scottish economy to benefit by tens of millions of pounds from the regular train line. The feasibility study will look at how the area can benefit from the railway. With a dedicated tourist service and the attraction of the Great Tapestry of Scotland to be based at Tweedbank, more people than ever will get to visit and enjoy Scotland's stunning Borders.
"There will be few railway journeys anywhere in Europe to match the outstanding scenery along the route of the new Borders Railway."
The First Minister also announced plans to introduce a steam train experience as early as September next year to help attract rail tourists to the Borders.
The Scottish Government believes the project will deliver a significant economic boost to the region. However, the development has previously been criticised by the Institute of Economic Affairs as "exceedingly poor value for money". It said that for every pound invested by taxpayers there would be only a 50p return.
Transport Minister Keith Brown said the benefits of public transport to the wider economy would outweigh the costs.
David Parker, leader of Scottish Borders Council, said: "The Scottish Government's commitment to steam and charter trains is extremely welcome and will be a fantastic boost to the Borders economy. The First Minister's pledge to work jointly with the Council to deliver the Great Tapestry of Scotland visitor centre and other improvements is fantastic news."
Mike Cantlay, Chairman of VisitScotland, said the new railway offered "a huge opportunity for Scottish tourism".
Simon Walton, chair of the Campaign for Borders Rail, said the line would be "an overwhelming success".