Mr Stevenson said the announcement was a "milestone" for the project
The timetable for the Borders rail line has been confirmed as the project was handed on to Transport Scotland.
Work is expected to start by 2011 and be completed by 2013 at a cost of between £235 and £295m.
Transport Minister Stewart Stevenson said the transition was a "milestone" and he expected "significant interest from a number of companies".
But the Scottish Building Federation expressed concern at the restrictions being placed on possible profits.
Its chief executive, Michael Levack, said: "What is the appetite for people coming forward and taking the risk on a venture like this when the Scottish Government has made it clear that they feel that in the past there's been excessive profits generated."
But Councillor David Parker, leader of Scottish Borders Council, called the announcement "a major milestone" in the rebuilding of the old Waverly route.
He added: "Other areas in the UK, with much smaller populations, continue to depend on their rail links. The future health of the Borders is depending, in part, on greater accessibility - both to the area, and to wider parts of Scotland."
The Waverley Railway (Scotland) Act 2006 received Royal Assent in July 2006. The line will serve a combined population of about 200,000 in the Scottish Borders and Midlothian.
Transport Scotland is the national transport agency of Scotland and is now expected to deliver the project in partnership with the rail industry.