The move, which will seek to capitalise on the vast visitor influx during the Edinburgh Festival, comes a month after The Scotsman’s revealed the plans.
Thousands of people also lined the route in May to see the steam locomotive Flying Scotsman make a special trip as part of its historic return to Scotland after a major refit.
The locomotive 46100 Royal Scot will haul the excursions in August and 60009 Union of South Africa - which operated last autumn’s trips on the line - will run the trains in September.
Return tickets between Edinburgh and Tweedbank are £55, or £130 for “premier dining”, or £150 for first class.
Passengers will travel on vintage carriages owned by the Bo’ness-based Scottish Railway Preservation Society.
The trips have been confined to Sundays - between 7 August and 25 September - to avoid the need to cancel regular ScotRail services because the line is largely single track. Fewer trains run on Sundays.
Last year’s sell-out trips included steam trains also running on Thursdays, which disrupted other passengers.
ScotRail commercial director Cathy Craig said: “This is a fabulous opportunity to showcase the line, and in such a romantic style.
“I look forward to seeing how successful these trips will be.”
Scottish Borders Council leader David Parker said: “The trips were extremely successful last year, with thousands of people visiting the Borders thanks to the journeys.”