Born in Caldogno, Italy, in the province of Vicenza, Veneto, he is the youngest of the eight children of Matilde and Fiorindo Baggio. Eddy Baggio is also the younger brother of the legendary Italian footballer Roberto Baggio, but unlike Roberto, Eddy never made his Serie A debut. Like several of his siblings, Eddy was named after a famous athlete, in his case the Belgian cyclist Eddy Merckx, whilst his older brother Roberto was named after two of his father's Italian footballing idols, Roberto Boninsegna and Roberto Bettega. Neither of the brothers are related to the former Italian defensive midfielder Dino Baggio.
Baggio started his youth and professional career at A.C. Fiorentina in 1991, the club where his older brother Roberto started to shine, and he was eventually promoted to the first team during the 1993–94 season, in Serie B.
He left the club 4 years after Roberto, and joined two different Serie C1 teams Palazzolo and Prato within two years. He then joined Serie C2 team Giorgione in November, and played there for 3 years. He then joined A.C. Ancona and Ascoli Calcio 1898 at that time in Serie C1.
He returned to Ancona in 2000 and made his Serie B debut during the 2000–01 Serie B season. In the following years, he changed club every season: Calcio Catania (Serie C1), Salernitana Calcio 1919 (Serie B), home-town club Vicenza Calcio (Serie B), Catania again (Serie B), Spezia Calcio 1906 (Serie C1), and he finally settled in Pisa. With Salernitana, on 15 December 2002, he scored his 100th professional goal in a 2–2 home draw against Serie B league leaders Triestina from a penalty; interestingly, his brother Roberto scored his 300th professional goal on the same day (their father's birthday), also from a penalty. On January 2008 he was sold to Serie C2 club Portosummaga, but managed to play only five times. On August 2008 he accepted an offer from Sangiovannese.
In total, he played 86 Serie B games, scoring 18 goals; throughout his career, he scored 130 goals in all competitions, including Serie B, Serie C1 & C2, the Coppa Italia, and the Coppa Italia Serie C, although he never played in Serie A.
Baggio represented the Italy Under-17 side on 3 occasions, and he represented the Italy team at the 1991 Under-17 World Championship.
From August 2011, he coached one of the Pisa "Allievi" youth formations. From the 2012–13 season, he became a coach for the Fiorentina youth side, coaching Fiorentina's Allievi Lega Pro. During the 2013–14 season, he was promoted to coach the Giovanissimi nazionali.Spezia
Coppa Italia Serie C: 2004–05