Tarquini's father ran a kart track and he began to compete at the age of eight. He was an accomplished kart racer, winning World, European and Italian titles. In 1983 he attended the CSAI racing school at Vallelunga and went straight into Formula 3, competing in six races in a Spreafico March-Toyota 803. The following year he did a couple of F3 races with Coloni, but went back to karting and won the World, European and Italian Championships. He won the Italian Marlboro Challenge and was immediately promoted into Formula 3000, in which he finished sixth in his first year. He also competed at Le Mans, sharing a Porsche 956B with Larrauri and Sigala, and was given a test drive by Benetton. In 1986 he competed once again in the F3000 Championship but there were few results. In 1987 he did a third season in F3000 with First Racing. That year he made his F1 debut at San Marino with an Osella-Alfa. He also drove in the WTCC, sharing a Beretta Brixia Motor Sport Alfa 75 Turbo with Rinaldo Drovandi.