Born in Bilbao, Biscay to Ghanaian parents, Williams spent much of his childhood in Pamplona and was playing youth football with local CD Pamplona when he was spotted by Athletic Bilbao, who signed him to their youth setup at Lezama at the age of 18. He spent his first season with the Juvenil A side and made a big impression, scoring at the rate of almost a goal a game ; the team finished runners-up in the Copa del Rey Juvenil de Fútbol, and on 25 June 2013 he signed a new contract with the Basque club, running until 2017. Williams began 2013–14 playing with CD Basconia, the farm team who competed in Tercera División. After suffering a knee injury in August, he returned to activity in October, made his debut as a senior and marked it with a goal. He was immediately called upon by the reserves in Segunda División B and by the end of the same month had played his first match and scored his first goals at that level; he spent the campaign alternating between both squads. At the start of 2014–15, Williams scored a hat-trick for Bilbao Athletic in a 4–0 win over SD Amorebieta, and followed this on 7 September 2014 with another treble in a 5–1 rout of SD Leioa. Despite only playing the first half of the season, his 13 goals from 18 appearances helped the team ascend to Segunda División. On 6 December 2014, after profiting from Aritz Aduriz's injury, Williams made his first-team – and La Liga – debut, starting in a 0–1 home loss against Córdoba CF. He netted his first goal on 19 February of the following year, starting and contributing to a 2–2 draw at Torino F.C. in the UEFA Europa Leagueround of 32, becoming in the process the first black player to score for the club. On 17 May 2015, Williams scored his first goal in the top flight, netting a last-minute winner in a 3–2 away success over Elche CF to help Athletic come from behind 0–2. Thirteen days later, he headed a consolation goal in the 1–3 loss to FC Barcelona in the final of the Copa del Rey at the Camp Nou. Williams scored a brace before giving away a penalty in Athletic's 3–1 win away to Real Betis, on 1 November 2015. He repeated the feat the following match, at home against FK Partizan in the Europa League group stage. Finding the net in his third match running, he scored "a phenomenal volley" to help beat RCD Espanyol 2–1 at the San Mamés. In late January 2016, having been scouted by the likes of Arsenal, Liverpool and Manchester City, Williams agreed to an extension of his contract until 2021. The deal included a €50 million buyout clause. He was sent off on 6 February at the end of a goalless home draw with Villarreal CF, together with opponent Daniele Bonera. During autumn 2017, Williams scored important late goals in the Europa League against Östersunds FK and Hertha BSC to help his team finish top of the group. On 17 January 2018, he agreed a contract renewal, running until 2025 with an incremental buyout clause of around €80 million. On 13 January 2019, Williams scored both goals in a 2–0 home league win over Sevilla FC, finding the net at San Mamés for the first time in 41 league appearances. His second, involving a turn and sprint from his own half, touch away from the goalkeeper and precise finish at high speed, was described as "incredible" – it was later awarded as the Marca Golden Goal of the season. The fixture was also his 100th successive appearance in the league, only the fifth Athletic player to achieve this and the first outfield player from any Spanish club to do so since Fran in 1993; for his performances, he was named the La Liga Player of the Month. Williams signed a nine-year contract in August 2019, with his release clause set at €135 million. Late in the same month he started and scored in a 2–0 Basque derby win for his 122nd consecutive Spanish League game, setting a new record by an outfield player in the 21st century. On 24 November, he repeated the feat in a 2–1 away victory against CA Osasuna, breaking a 31–game undefeated streak of the hosts at their El Sadar Stadium; the occasion also marked his 133rd consecutive appearance in the Spanish top level, establishing a new club record previously held by Carmelo Cedrún.
Williams' younger brother, Nico, is also a footballer and a forward. He too was brought up at Athletic Bilbao. Williams was one of the stars of the Amazon Prime television documentary series Six Dreams, recorded during the 2017–18 season.
