He was a member of the Sweden squad that reached the quarter-finals of the 2018 FIFA World Cup, and also represented his country at UEFA Euro 2016 and 2020, the latter of which he scored four goals in four games.

He is known for his quick, effective passing style, and is a creative playmaker renowned for his ability to create chances and assists.

He also participated in all of the club's matches in the 2014–15 UEFA Champions League campaign in which Malmö FF qualified for the group stage.

[5] In January 2015, Forsberg joined German second league side RB Leipzig on a three-and-a-half-year deal.

[10] On 13 September 2017, Forsberg scored RB Leipzig's first ever Champions League goal in their first match ever in a 1–1 draw against Monaco.

[11] In the 2019–20 season, he scored a brace in the stoppage time in a 2–2 draw against Benfica, to secure a place for RB Leipzig in the 2019–20 UEFA Champions League knockout phase,[12] where they managed to reach the semi-finals until they lost to Paris Saint-Germain.

[14] On 24 February 2022, he scored a penalty in the 89th minute to secure a 3–1 away victory over Real Sociedad during the Europa League knockout round play-offs, which marked the 1000th goal in club's history.

[15] In his final home match for Leipzig on 16 December 2023, Forsberg came off the bench and scored the game winner and assisted another goal in a 3–1 victory over Hoffenheim.

On 16 December 2023, Major League Soccer side New York Red Bulls announced that Forsberg would join the club in 2024, signing a contract until 2026, with an option for a further year.

[17] On 25 February 2024, Forsberg made his debut for New York, appearing as a starter in the opening match of the season, a 0–0 draw against Nashville SC.