Mr Swinney also marked the occasion of the roof being completed at the £16.78 million facility by signing a steel beam.
Speaking at the event, he said: "This new school will give local children and young people a modern learning environment that they and their families can be proud of. The leisure facilities, library and café will also make it a hub for people in the surrounding area, in line with our vision for schools being the centre of their communities.
"My thanks to Midlothian Council for their ongoing commitment to improving school buildings and congratulations to them and the construction staff on reaching this terrific milestone."
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Main contractor Heron Bros is delivering the state-of-the-art building, which will be able to accommodate 640 pupils and 120 children in its three nursery spaces.
As well as a new primary school and early learning centre, the new build will have a library, leisure centre, cafe and sports pitches.
The building, on the site of the existing primary school, is planned to open in the autumn of 2020.
The multi-million investment is in addition to more than £150 million spent in the last ten years on building new or upgrading existing schools across Midlothian.
Midlothian Council's Cabinet Member for Education, Cllr Jim Muirhead also said: "I'm delighted to be here today to welcome Mr Swinney and mark this important milestone in this fantastic project.
"The new building at Danderhall will be a much-needed addition to our schools and community estate. We are all really looking forward to the opening in August and the building becoming a busy and well-used focal point for local people."
The redevelopment of the site comes after extensive consultation with local people and pupils like Hazel and Max pictured, about preferences for the school and community facilities. Hazel and Max, who also got to sign the girder, said they were excited to think their signatures would be on the building for as long as it was up even though they will be in high school when it opens.
(MH/CM)
