Born in Mechelen, Limbombe began his youth career with Mechelen in 2000. In 2005, he joined Belgian Pro League side Racing Genk. He made his first team debut at the age of 16 in a 3–1 victory at Lokeren on 18 September 2010. He also played for Genk in the Champions League and the UEFA Europa League. During his career with Racing Genk he won the Belgian Pro League in 2010/11 season, and he also won the Belgian Supercup in 2011, in total he scored 2 goals in 62 League appearances.
The second half of the 2013–14 season, Limbombe was sent on loan to Lierse SK where he scored 2 goals in 7 games.
On 30 August 2014, he signed with Eerste Divisie side NEC Nijmegen on a three-year deal with the option of a fourth year. He impressed in his first season at the club, scoring an 14 goals and providing numerous assists in his debut season at the club, helping NEC Nijmegen win the Eerste Divisie as champions and gain promotion to Eredivisie.
On 12 August 2015, Limbombe played for NEC Nijmegen against Excelsior in the opening day of the Eredivisie 2015/16 season in a 1-0 victory. On 13 August 2015, NEC Nijmegen rejected a £1.5 million bid from English side Leeds United for Limbombe. On 22 August, NEC Nijmegen announced that Limbombe had been left out of the squad against Ajax due to deeming him 'insufficiently focused' after the interest linking him with Leeds United. However, on 1 September, Leeds ended their interest in Limbombe after failing to up the bid, they signed Winger Jordan Botaka from Dutch Club Excelsior instead.
After impressing during the 2015/16 season, scoring 7 goals and gaining 7 assists in the Eredivisie, on 1 June 2016, Limbombe amid further interest from English side Leeds United handed in a transfer request at NEC Nijmegen.
On 23 July 2016, Limbombe returned to Belgium to join Club Brugge on a four-year deal for a fee around the margin of £2 million.
Limbombe who is eligible to represent both Belgium and DR Congo. He represented Belgium at U16 international level and has played at Belgium U17 level. In 2012, he was capped for Belgium U19's.
Anthony is the younger brother of the footballer Stallone Limbombe.As of match played 8 May 2016.
Racing GenkBelgian Pro League: 2010–11
Belgian Supercup: 2011
NECEerste Divisie (1): 2014–15
Limbombe's older brother Stallone Limbombe is also a professional footballer and is playing as a creative winger for Antwerp FC.