Jackson scored his first professional goal on 28 November 2020, netting the opener in a 1–1 home draw against CD Castellón.[15] It was his only goal of the season as the Jabatos finished in 10th place.
Jackson scored his first goal in the top tier on 13 August 2022, netting the opener in a 3–0 away win over Real Valladolid. Thirteen days later, he and teammate Álex Baena were promoted to the main squad.[17]
In January 2023, Villarreal agreed a £22.5 million deal from AFC Bournemouth for the signing of Jackson but he failed his medical due to hamstring issues.[18] After returning to action in March, he scored nine goals within the months of April and May, which included braces against Celta de Vigo, Athletic Bilbao and Cádiz.
Chelsea
On 30 June 2023, Jackson signed for Premier League club Chelsea on an eight-year deal through 2031 for a fee reported to be £32 million.[19] On 13 August, he made his debut for the club in a 1–1 draw against Liverpool in the Premier League.[20] Jackson scored his first Chelsea goal on 25 August 2023 against newly promoted side Luton Town, helping Chelsea to a 3–0 win at Stamford Bridge.[21] He scored his second Chelsea goal in a 1–0 win over Brighton & Hove Albion in the EFL Cup.[22] On 6 November, Jackson scored twice in second-half stoppage time to complete a hat-trick in a 4–1 away win over Tottenham Hotspur.[23] He scored again in the next match against Manchester City, which ended in a 4–4 home draw.[24]
On 15 April 2024, Jackson scored his tenth Premier League goal of the season as well as providing an assist for Cole Palmer in a 6–0 win over Everton. As Palmer had already reached double digits in league goals, this became the first Chelsea season since 2017–18 in which two players had scored ten or more Premier League goals in a season.[25]. On 5 May 2024, Jackson scored his first brace for Chelsea as well as providing an assist for Cole Palmer in a 5-0 home win over West Ham.[26]
Despite the heavy criticisms he faced in his first season in Chelsea, Jackson managed to score 14 Premier League goals in 35 appearances to make him the second highest African goal scorer in the 2023–24 season only behind Mohamed Salah.[27]
After being called up to the full side by manager Aliou Cissé for two friendlies in September 2022, Jackson was included in the 26-man list for the 2022 FIFA World Cup on 11 November 2022.[31] He made his full international debut in Senegal's opening match of the competition, replacing Krépin Diatta in a 2–0 loss against the Netherlands.[32]