Jonsson was part of a contingent of Swedish motorcyclists including; Bill Nilsson, Rolf Tibblin and Torsten Hallman who dominated the sport of motocross in the 1960s and early 1970s.

[7][8] His impressive results earned him a sponsorship to ride for the Husqvarna factory and with a new motorcycle, Jonsson was able to defeat Torsten Hallman for the 1964 250cc Swedish national championship.

However, his motorcycle had a mechanical failure at Round 10 in Belgium allowing BSA factory rider John Banks to claim the championship points lead.

[17] In 1969 Jonsson was hired to ride in the 500cc class for the Maico factory racing team alongside teammates Adolf Weil and Willy Bauer however, his motorcycle had reliability issues and he dropped to 13th in the season final points standings.

[7] In the 1970 season he began to post consistent results and won the East German Grand Prix and placed second in Belgium to take the championship points lead going into the final round in Luxembourg.

[20] Jonsson's best year would be in 1971 where his main rivals for the 500cc World Championship would be his Maico teammate Adolph Weil and Suzuki factory team rider, Roger De Coster.

[6][21] Jonsson had taken the lead at the beginning of the final round when his motorcycle's spark plug came loose, allowing DeCoster to pass him for the victory and claim the World Championship by a four point margin.

[21] A few weeks later he took a slight revenge by winning both motos to lead the Swedish team to their second consecutive victory at the 1971 Motocross des Nations held in Vannes, France.

[6][27][28] For the 1973 season, Jonsson was hired for three years, by the Yamaha to ride their new motorcycle with its innovative rear suspension using a single shock absorber called a monoshock.

[5] When he first joined the Yamaha team, it was rumored that he installed Maico front suspension to his bike but, Jonsson stated in a later interview that the forks were manufactured in Japan.