Tesser, a defender, started his playing career with Treviso. He moved to Napoli in 1978, where he played two seasons. He then played for Udinese from 1980 to 1985, and then for some lower league teams, including Perugia and Catania. He was also capped for the Italian U-21 side.
Tesser started the 2007-08 season at the helm of Serie B side Mantova, with the aim to fight for a promotion spot; however, results did not confirm the initial goals, and he was sacked on February 24, 2008, leaving Mantova in seventh place, seven points far from the fourth playoff spot.
On January 2009 he accepted a coaching offer from Lega Pro Prima Divisione club Padova; however, his stint with the patavini lasted only one month, as he was sacked later on February.
On June 2009 he was named Novara manager. His tenure proved to be highly successful, as he led his club to become Lega Pro Prima Divisione champions in his first season in charge. In the 2010–11 season, Tesser repeated himself as he guided Novara to third place in the final table, then winning a second consecutive promotion to Serie A after defeating Reggina and Padova in the playoffs. The Serie A comeback however proved to be particularly difficult for Novara, who only managed to win 12 points after the first 20 games: this cost Tesser the job, as he was removed from his managerial duties on 30 January 2012 following a 2-0 away loss against Palermo; he was replaced by veteran coach Emiliano Mondonico. On 6 March 2012 he was recalled by Novara as head coach, but on 31 October 2012 he was again sacked.