Angelo Colombo began his career with the Monza in 1979, first with the youth squad, at the age of 13, and later making his professional debut with the club in Serie B. In 1984, he was acquired by Pierpaolo Marino's Avellino side, and he made his Serie A debut with the club on 16September 1984, in a 0–0 home draw against Roma. The following season, he transferred to Udinese, in 1985, and in 1987, he was bought by Milan, under manager Arrigo Sacchi, making his club debut in the Coppa Italia on 23 August 1987, in a 5–0 win over Bari. He enjoyed a successful three-season spell with Milan, winning the 1987–88 Serie A title, the 1988 Supercoppa Italiana, consecutive European Cups, as well as the 1989 Intercontinental Cup, and the 1989 European Super Cup, with his final appearance coming in Milan's 1–0 victory over Benfica in the 1990 European Cup Final on 23 May; in total he made 115 appearances for the club between 1987 and 1990, scoring 7 goals, all of which came in his 77 Serie A appearances with the club. In 1990, he moved to Bari, at the request of Salvemini, to replace Carbone, who had recently been purchased by his former club Milan. In 1992, he left the club, temporarily retiring from football, although in 1994, he returned to football, signing for Australian side Marconi Stallions, with whom he ended his career after the 1994–95 season.
After retiring, Colombo coached the Milan youth side for five years, and later became a their co-ordinator for four more years, and subsequently a scout for the team. On 26 January 2009, he signed a contract to coach Montebelluna in Serie D, replacing Gianfranco Borgato, and saving the team from relegation in the play-off against Somma. In May 2010, he took charge of Carpendolo during the 2009–10 Lega ProSecond Division play-offs against Villacidrese, which ended with the club's relegation to Serie D at the end of the season. The following season, the team were defeated in the Serie D play-off against Mobilieri Ponsacco, but the team were not relegated to the Eccellenza League, as they were re-drawn. On 30 October 2011, Colombo was sacked, as the team were second last during the 2011–12 Serie D season.