Ukraine's security chief Valentyn Nalivaychenko said the crossing of the border marked a "direct invasion by Russia of Ukraine", Reuters reported. The country called on its international partners to unite in a "decisive condemnation of illegal and aggressive actions".
Read MoreMoscow defies Kiev, aid convoy passes Ukraine border
The Russian trucks are headed to the city of Luhansk in eastern Ukraine – a pro-Russian rebel stronghold.
By 3:00 p.m. London time, the French CAC 40 traded around 0.5 percent lower, recovering from its lows earlier in the afternoon as Yellen said the U.S. economy was getting closer to the Federal Reserve's objectives at a meeting of central bankers in Jackson Hole, Wyoming.
The German DAX - thought to have the most exposure in Europe to Russia - was down 0.6 percent, and Britain's FTSE 100 was flat, paring some losses. The pan-European FTSEurofirst 300 was down 0.1 percent.
"Markets have a memory of what happened last week – things were going swimmingly and then everything was thrown off because of geopolitical developments," said Jasper Lawler, market analyst, at CMC markets.
"The Germany DAX is particularly vulnerable because of its trade ties to Russia, and so is Europe as a whole."
U.S. stocks wavered between modest gains and falls, although the S&P 500 fluctuated near its record high, as Yellen spoke.
The price of Treasurys – seen as a safe haven moved higher on Friday. The yield on benchmark 10-year Treasury notes—used to calculate mortgage rates and other consumer loans—was around 2.413 percent.
Read MoreYellen could be the one to kick the S&P to 2,000
Russian stocks hit