His route into motorsport came through Swedish Folkrace, a popular and affordable regional form of rallycross. He started in rallying alongside fellow Swede Per-Gunnar Andersson (no relation) in 2002. By 2004 they had won the FIA Junior World Rally Championship (JWRC), a title they claimed again in 2007.
In 2006, Andersson co-drove a ŠKODA for the first time, with Mattias Ekström, at the Rallye Deutschland. Alongside Per-Gunnar Andersson, he also co-drove the same car to two victories in Norway in 2008 and 2009 respectively.
In 2009, funding problems of PG Andersson saw Jonas switch to co-drive alongside Norwegian Mads Østberg. They won the Norwegian Rally Championship in 2011, and in 2012 enjoyed a maiden FIA World Rally Championship (WRC) event victory at the Rally de Portugal.
By 2016, feeling the need for a new challenge, Andersson opted to join ŠKODA Motorsport as co-driver to fellow Swede Pontus Tidemand. Together they have won one round of the WRC2 Championship to date, the Rally de Portugal 2016.
Andersson is sitting alongside Pontus Tidemand in the ŠKODA FABIA R5 once again in 2017.
Czech National Championship
2 podiums: Rallye Český Krumlov, Rallye Šumava Klatovy