The shop, which already handles Skoda's UK advertising, won the account after beating Leagas Delaney Prague and 18 Feet & Rising in the final pitch.
Amsterdam Worldwide and Kaspen/Jung von Matt were involved at an earlier stage.
Fallon will now establish an office in the city of Skoda's headquarters to service the business.
The European Union-wide account is thought to be worth an estimated €3.5 million (£2.85 million) in fees alone.One of Fallon's first tasks will be to help launch Skoda's new Fabia model later in the year.
Leagas Delaney Prague, the incumbent, has held the business for about ten years. The agency's Hamburg office will continue to handle Skoda's advertising in Germany.
Meanwhile, 18 Feet & Rising is being considered for a place on the roster for Skoda's owner, Volkswagen.
James Townsend, the managing director at Fallon, said: "We're delighted to take this next step with Skoda – as our oldest client in the UK, we have a special relationship with the brand.
"We are also thrilled to be opening up in Prague, where we hope to deliver world-class creative work for Skoda across the globe."
Fallon has overseen Skoda's UK advertising since 1999 and created spots including "cake", which won a gold Lion at Cannes in 2008.
MediaCom handles media planning and buying duties for Skoda as well as other brands in the Volkswagen portfolio.