Robertson won the contract through Hub East Central Scotland Ltd, a £500m investment programme from the Scottish government covering construction projects throughout Forth Valley, Fife and Tayside.
Redwell Primary is being built to replace the existing St John's and Claremont Primary Schools and will have capacity for more than 430 pupils with room for further expansion if required. It is due to open in August 2014.
Robertson Construction managing director Derek Shewan said: "We look forward to working in partnership with Clackmannanshire Council and the local community to deliver a project which will affect the lives of many of the region's young people.
"As part of our delivery of the new school, we are also looking forward to creating training and career opportunities for local people - further evidence of the new school's long-lasting impact on the community."