Peebles High School is closed until after the Christmas holiday following the blaze on Thursday 28 November.
At its height, up to 70 firefighters were in attendance as they worked overnight to contain the fire. Art classrooms, a gymnasium and surrounding areas suffered "significant damage."
Mr Swinney thanked the emergency services and the council for their work over the last week and said the Scottish Government will be as supportive as it can.
New photos of the building were released showing the extent of the damage.
Education Secretary John Swinney spoke of the issue in in Holyrood on Tuesday. He said: "Presiding officer my thoughts are with pupils staff and parents at Peebles High School following the fire at the school and I pay tribute to the resilience of everyone dealing with this challenging situation.
"I also pay tribute to our emergency services for their prompt action in addressing this very serious incident.
"The Scottish Government remains in close contact with Scottish Borders Council and stand to provide any support necessary to minimise disruption to pupil's learning.
The council has stated that all pre-Christmas preliminary exams have been postponed until the new year to ensure pupils have the opportunity to be fully prepared for these important examinations."
In a Tweet, Mr Swinney said: "Grateful for visit and briefing on the devastating fire at Peebles High. Pleased that face to face education will start on Monday. Made clear the Scottish government will work with the Council and the school to recover from this serious situation."
More than 1,000 pupils are expected to return to "face-to-face" teaching in the next week, and senior students will be taught by teachers from the school but will have to travel to Galashiels.
The council say they are still finalising plans for pupils in S1 and S3.