The money will cover 80% of the total cost of the schemes in Brechin, Angus, and Selkirk in the Borders.
The Scottish Government is also contributing £500,000 towards the cost of fixing damage caused by severe tides and flooding in Dumfries and Galloway earlier this year.
The one-off award will help pay for repairs to river banks, sea walls and coastal paths.
Environment and Climate Change Minister Paul Wheelhouse said: "Communities living under threat of flooding know only too well the devastating effects it can have - as recently seen in Dumfries and Galloway. That is why flooding remains a priority for the Scottish Government.
"More than £38.5m Scottish Government funding for new flood protection schemes in Brechin and Selkirk - a significant investment, which will allow the councils involved to start the tendering process and bring these schemes to fruition.
"I look forward to seeing the undoubted positive impact of these works for residents and businesses in these communities." Under the flood protection scheme funding arrangement agreed with Cosla, 80% of the total cost of approved projects is funded by the Scottish Government, with the remaining 20% funded at local authority level.
The £31.8m Selkirk Flood Protection Scheme will protect around 650 properties against flood events from the Ettrick and Yarrow Waters, the Philiphaugh Mill Lade, the Long Philip Burn and the Shaw Burn.
Construction is due to get under way in autumn 2014 and is scheduled to conclude in late 2016.
The Brechin project, which will cost £16.4m in total, will protect around 150 properties and consist of direct defences, flood embankments and flood walls, drainage system upgrades and three submerged pump stations.