He won the F.I.M. 250cc Motocross World Championship in 1979 as a member of the Husqvarna factory racing team. In 1980, he switched to Yamaha to contest the 500cc motocross world championship. He finished 3rd in 1981 and 1982. In 1983, he battled against Honda teammates André Malherbe and Graham Noyce to claim the 500cc world championship, on a Yamaha. In 1984, an injury stopped Carlqvist from contesting the title again. He raced for Yamaha until end of 1986. He continued the 500 GPs in 1987 and 1988 with a privateerKawasaki KX500. His last Grand Prix victory was the Belgian Grand Prix at Namur in 1988. During this race, he stunned the spectators by stopping before the end of the 2nd moto to drink a beer, while leading the race by somewhat 50 seconds, and going back into the race to win it.