Kopecký initially competed as a circuit touring car driver before switching to rally sport in 2001, winning national sprint rally championships in his early years. By 2004 he had taken the national classical rally title and entered the World Rally Championship the following season.
In the 2006 WRC season, Kopecký competed with co-driver Filip Schovánek in a Škoda Fabia WRC. He won three special stages across that season — at the Rally d'Italia Sardegna and the Rallye Deutschland — and achieved his best overall finish of fifth place at the Rally Catalunya, scoring 7 championship points and placing fifteenth in the drivers' standings. He continued with the Fabia in 2007, improving to twelfth in the championship with a best finish of fifth at the Rallye Deutschland.
In 2008, Kopecký made a brief foray with a Fiat Grande Punto Abarth S2000 at Rally México before switching to a Peugeot 207 S2000 and the Intercontinental Rally Challenge circuit. After strong results drew Škoda's attention, he was signed by Škoda Motorsport and began testing the Fabia S2000.
Kopecký quickly established himself as a frontrunner in the IRC driving the works Škoda Fabia Super 2000. In 2009 he finished second in the IRC championship, winning the Rally Principe de Asturias and the Barum Czech Rally Zlín — making him the first Czech driver to win the Barum rally in a Czech car. The championship went to Kris Meeke.
In 2010, he won the Rally Islas Canarias and finished second at both the Ypres Rally and the Rali Vinho da Madeira, but two retirements from the lead — at the Rally Azores and the Barum Rally Zlín — cost him dearly. He again finished second in the IRC standings, this time behind his Škoda Motorsport team-mate Juho Hänninen.
Kopecký secured the 2013 European Rally Championship title, one of the most prestigious prizes in the sub-WRC category. He remained a central figure in Škoda's rally programme through the following years, ultimately adding the 2018 WRC-2 championship to his resume. He also claimed the Asia-Pacific Rally Championship title, rounding out a career that saw him collect major honours across every significant regional and sub-world category.
Jan Kopecký is regarded as one of the most successful rally drivers in Czech motorsport history and among the most decorated competitors in the IRC and ERC eras. His longevity with Škoda Motorsport made him a cornerstone of the marque's international rally identity, and his ability to extract competitive results across multiple championship formats over more than two decades places him among the most complete drivers of his generation below the WRC top tier.