[3] Jonsson came to prominence after helping his first club Getingarna win the Swedish Speedway Team Championship in 1982.

Following the end of the 1988 season he returned to Getingarna, now known as Stockholm United and won a fifth Swedish league championship.

Sweden, whose lineup was Jonsson, Henrik Gustafsson, Jimmy Nilsen, Tony Rickardsson, Conny Ivarsson, Erik Stenlund and Peter Nahlin defeated the Phil Crump captained Australia (who fielded 14 riders over the series) 3–2 in the five match series with Jonsson topping the averages for both teams with 16.4 per test.

His 1992 Individual Speedway World Championship got off to a bad start in Wrocław, Poland, when he failed to score in his first ride.

[11] His career was cut short when a crash during a league meeting in Poland in 1994 left him using a wheelchair for the rest of his life.

His son Dennis Jonsson rode for Lakeside Hammers in the 2016 Elite League but retired from speedway following a serious accident when riding for Marsana in Sweden.