The main construction works contract worth £31.4m is due to start in January and finish by the end of December 2016.
It is one of the largest procurement contracts ever let by the Scottish Borders Council and will protect 650 properties against flooding from the Ettrick and Yarrow Waters and Long Philip and Shaw burns.
Councillor Gordon Edgar, Scottish Borders Council’s Executive Member for Roads and Infrastructure, said: “The announcement that RJ McLeod has been selected as the successful tenderer is another big step forward for the Flood Protection Scheme and the town of Selkirk.
“On behalf of the Council, I look forward to the commencement of the site works in 2015.”