Born in Ondarroa, Biscay, Basque Country, Arrizabalaga joined Athletic Bilbao's youth setup at Lezama in 2004, aged ten.

[5] On 5 May 2012, Arrizabalaga was called up to the main squad for a La Liga match against Getafe,[6] but remained unused in the 0–0 draw at the San Mamés Stadium.

[10] On 3 March, he was one of two players sent off towards the end of a 3–1 home win over Amorebieta, as well as teammate Jon García;[11] in April he suffered a pubalgia, only returning to the field in September.

On 11 March, Getafe submitted a loan request to the Lions for him, as a replacement to injured Miguel Ángel Moyá,[14] but it was rejected a day later.

[21] On 22 January 2018, amid heavy transfer speculation linking him to Real Madrid, Arrizabalaga renewed his contract – due to expire that June – until 2025.

[29] On 24 February 2019, during the 2019 EFL Cup Final against Manchester City, with the match at 0–0 near the end of extra time, Maurizio Sarri called for Arrizabalaga to be substituted off for Willy Caballero for the upcoming penalty shootout.

On 9 May 2019, Arrizabalaga saved two penalties in the shootout at the end of the second leg of the UEFA Europa League semi-final against Eintracht Frankfurt to take Chelsea to the final,[35] which they won 4–1 over Arsenal.

Throughout the 2019–20 season, Arrizabalaga struggled to stay in form, eventually being benched in favour of Willy Caballero in late January 2020 in a cup match against Hull City.

[37] He regained his starting spot on 4 March during the FA Cup fifth round against Liverpool where he made a string of saves to deny the eventual Premier League champions;[38] Chelsea went on to win the match 2–0.

Arrizabalaga was judged to have made a significant error in the next match against Liverpool, after his pass went straight to Sadio Mané who collected the ball and scored; Chelsea went on to lose 2–0.

[46] He was named as part of the 25-man squad for the 2021 UEFA Champions League Final on 29 May, and was an unused substitute as Chelsea beat Manchester City 1–0 at the Estádio do Dragão, lifting his second European trophy.

He saved two penalties, including the decisive attempt from Villarreal captain Raúl Albiol, in the shootout as Chelsea won their second Super Cup title.

[50] Later in the season, Arrizabalaga started only a few matches including league cup tie against Aston Villa, which Chelsea would go on to win 4–3 on penalties after a 1–1 draw.

He kept his place in the squad with a run of five consecutive clean sheets, including impressive away displays at Aston Villa and Brentford, the latter of which being his 50th for Chelsea.

[56] Following the turn of the year, he won three back-to-back Man of the Match awards, following clean sheets against Crystal Palace, Liverpool, and Fulham.

[64] On 25 August 2023, Kepa made his debut for the club in a 1–0 away win over Celta Vigo, simultaneously keeping his first clean sheet for Carlo Ancelotti's side.

[69] Kepa's final appearance of his loan spell came as a substitute on the last day of the La Liga season, playing 27 minutes against Real Betis at the Estadio Santiago Bernabéu.

[70] Kepa returned to Chelsea at the end of the season, having played twenty matches for Real Madrid and winning the La Liga, Supercopa de España and UEFA Champions League titles.

[80] Arrizabalaga was called up to the senior side on 22 March 2017 ahead of a 2018 FIFA World Cup qualifier against Israel and a friendly with France, as a late replacement for the injured Pepe Reina.

"[92] Following a strong start to the first part of his debut season with Chelsea, Arrizabalaga came under criticism for his inconsistency and poor performances, as well as his low save-percentage.

He finished the season with the worst save percentage in Premier League history,[100] an unwanted record eventually broken by Gavin Bazunu of Southampton.