De Agostini was born in Udine. His professional career began with his hometown club, Udinese, making his debut in a 0–0 draw against Napoli on 23 March 1980. He was rarely played during his time at the club, forcing him to move to Serie C1 for Trento for a year. He was immediately back in the Serie A next year, however this time for Catanzaro before he moved back to Udinese, this time much more prominent. In 1986, he was signed on for Hellas Verona, though it would only be the following year that he would achieve his greatest success, signing with Juventus in 1987.
During his five-year stay with Juventus, as well as taking on his usual defensive role, he was also often employed as a box-to-box midfielder, due to his offensive and defensive work-rate and contribution. Despite his defensive style of play, he was awarded the coveted number 10 shirt, following Michel Platini's retirement. With the club, he won both the Italian Cup and the UEFA Cup during the 1989–90 season. He scored for Juventus as they beat rivals Fiorentina in the 1990 UEFA Cup Final. Despite being an accurate penalty taker, he is also remembered for missing a penalty against Fiorentina the following season, after Roberto Baggio had refused to take a penalty against his former club. With Juventus, he managed 28 goals in 217 appearances.
After his time with Juventus, Luigi moved to Inter Milan for a year, then transferred to Reggiana in 1993, ending his professional career after two seasons with the club. In total, over his 15 seasons of his professional career, he made 378 appearances in Serie A, scoring 33 goals.
During his time with Juventus, De Agostini achieved his first senior international cap in a 0–0 draw against Norway on May 28, 1987. With Italy, he participated in Euro '88, scoring against Denmark, as Italy went on to reach the semi-finals. He also took part in Italy's footballing campaign at the 1988 Summer Olympics, where they managed a fourth-place finish after reaching the semi-finals yet again. He was also a substitute member of Italy's squad at the 1990 World Cup on home soil, where the team managed a third-place finish following a penalty-shootout defeat to defending champions Argentina; despite the loss, De Agostini was able to net his penalty in the semi-final shoot-out. Under manager Azeglio Vicini, he was also often deployed as a wide midfielder or as a wing-back, in addition to his more regular full-back role. Unfortunately, his time with Juventus also included his last game for the Italian national team on September 25, 1991, in a 2–1 home loss to Bulgaria, during Italy's qualifying campaign for Euro 1992. In total he made 36 appearances for Italy, scoring 4 goals.
De Agostini was a tactically versatile and hard-working defender, who could play anywhere along the left flank, or even in the centre, due to his ability to assist his team both offensively and defensively. He was primarily deployed in the role of an attacking left-back or wing-back, due to his pace, stamina, marking, crossing, positional sense, technical ability, and his capacity to read the game. He was also capable of playing anywhere in midfield, and was also used on the wing, in a box-to-box role, or even in the centre as a defensive midfielder, due to his anticipation and tenacious style of play. In addition to his defensive attributes, De Agostini was known to be an accurate penalty taker.Juventus
UEFA Cup: 1989–90
Italian Cup: 1989–90
Mitropa Cup: 1979–80
Serie B: 1978–79
FIFA World Cup: 1990 (Third Place)
5th Class/Knight: Cavaliere Ordine al Merito della Repubblica Italiana