The yield, or the return on investment to investors, on ten-year Bunds fell to 0.098 percent in early trading on the secondary market, compared to 0.188 percent at the close on Tuesday.
Meanwhile the yield on ten-year French government bonds fell to 0.430 compared to 0.500 percent.
"The election of Donald Trump seems to trigger a risk-off mode," said analysts at BNP Paribas bank.
Meanwhile analysts at ING Bank said: "We expect a risk off move for the next few days... the ten-year Bund yield might drop towards the 0.05 percent area."
Market turbulence may also prompt the US Federal Reserve to hold off on raising interests rates in December, which would also influence investors willingness to hold lower-yield assets.
"Given the adverse market reaction we have already seen, the Fed's planned December rate hike is now off the table," Capital Economic's chief US economist Paul Ashworth said.
Bonds from southern European countries, seen as more risky, saw their yields climb.
Italian ten-year bonds rose to 1.744 percent from 1.721 percent.
Spanish ten-year bonds climbed to 1.270 percent from 1.254 percent.
The yields on US bonds also fell in electronic trading before market opening.
Ten-year treasury bonds fell to 1.810 percent from 1.855 percent on Tuesday. The yield on 30-year bonds fell to 2.682 percent from 2.620 percent.