The rate of return to investors on 10-year Spanish government bonds fell to 1.231 percent from 1.275 percent on Monday.
The yield on 10-year Italian government bonds fell to 1.220 percent from 1.280 percent and those of Germany fell to 0.279 percent from 0.312.
The European Central Bank launched on Monday a so-called quantitative easing (QE) programme that will see it buy €60 billion of eurozone government and corporate bonds through next September.
The ECB hopes that by buying bonds off investors they will invest the money elsewhere, thus boosting growth and preventing a dangerous cycle of falling prices from setting in.
Eurozone bond yields have been falling in recent weeks to record lows as investors anticipated the increased demand from ECB purchases.
The yield on French 10-year bonds was at 0.568 percent in morning trading, above the record low of 0.521 percent set in January.
Greek bonds are not benefitting from the decline in yields due to a new spike in concerns over its finances as well as Greek debt not being included in the QE programme.