TSA have accepted his decision to leave with immediate effect and thanked De Jager for "his nine years of dedication to TSA and South African tennis".
"We further wish him all the best for the future," TSA said in a statement.
"Our president and acting chief executive officer, Gavin Crookes, is currently out of the country and a meeting will be convened as soon as he returns. A detailed reply will be formulated later this month."
TSA said it was an urgent priority to find a replacement captain with the Davis Cup tie against Turkey coming up from March 6 to 8.
Source: Sapa
