Growing up in Finland, Saros played his entire youth career and first three professional seasons with his hometown club, HPK of the Liiga.

Upon concluding the 2014–15 season, Saros joined the Nashville Predators organization in North America and was immediately assigned to their American Hockey League affiliate, the Milwaukee Admirals.

[5] While Saros was born in Forssa, he played his entire youth career and first three professional seasons with his hometown club HPK of the Liiga.

The school enabled him to take morning courses, allowed for extended absences due to hockey, and helped him to graduate in three years.

[8] During his 2011–12 season with the HPK Jr. team in the U18 SM-sarja, Saros maintained a 2.53 goals against average (GAA) and .910 save percentage (SV) through 31 games.

[9] He then represented Team Finland for the first time on the international level at the 2012 IIHF World U18 Championships as a backup goaltender for Joonas Korpisalo.

[10] In August, he represented Team Finland at the 2012 Ivan Hlinka Memorial Tournament where he helped them win a silver medal.

[6] In April, Saros was again selected to represent Team Finland at the 2013 IIHF World U18 Championships, where he outperformed nearly every goaltender at the tournament.

[12] Due to his performance at both the local and national level, Saros was considered the best European goaltender available at the 2013 NHL Entry Draft.

[15] After the season concluded, Saros was named to his first senior level tournament with Team Finland although he never played in the 2014 IIHF World Championship.

[16] In June 2014, Saros began his mandatory military service in Finland but was temporarily allowed to compete in USA Hockey's National Junior Evaluation Camp.

[17] Upon concluding the 2014–15 season in Finland, Saros signed a three-year, entry-level contract with the Nashville Predators to begin his professional career in North America.

[6] After attending the Predators training camp, Saros was assigned to their American Hockey League (AHL) affiliate, the Milwaukee Admirals, to begin the 2015–16 season.

[21] Saros picked up another five game winning streak in late February and early March while also leading all rookies with a 2.34 goals-against average.

[34] While remaining at the NHL level through January, Saros recorded a career-high 35 saves on the way to his fourth victory of the season in a 2–1 win over the Boston Bruins.

[38] Saros later tied his career high 35 saves, including 19 in the first period alone, to lift the Predators to a 4–3 win over the Columbus Blue Jackets on 19 February.

[41] As the Predators clinched a spot in the 2017 Stanley Cup playoffs, Saros finished the regular season with a 10–8–3 record, a 2.35 goals-against average, and .923 save percentage in 21 games.

[42] He served as backup to Pekka Rinne throughout the Predators playoff berth and did not play a minute until the 2017 Stanley Cup Finals.

[61] During the playoffs, Saros did not allow a goal in 65:11 before replacing Rinne in Game 7 of their Western Conference Second Round matchup against the Winnipeg Jets.

[67] A few months later, on 25 March, Saros made 29 saves in a win over the Minnesota Wild to help the Predators clinch a berth in the 2019 Stanley Cup playoffs.

[73] As the Predators continued to struggle to win games, the team fired head coach Laviolette in early January and replaced him with John Hynes.

[72] When the NHL resumed play and the Predators faced the Arizona Coyotes in the 2020 Stanley Cup Qualifiers, Saros was tapped as the starter for Game 1.

The Predators were also sequestered into the Central Division and only competed against the Carolina Hurricanes, Chicago Blackhawks, Columbus Blue Jackets, Detroit Red Wings, Florida Panthers, Dallas Stars, and Tampa Bay Lightning.

[85] He continued to find success through the remainder of the week and compiled a 3-0-0 record, 0.67 goals-against average, .976 save percentage, and one shutout.

[87] On 8 May, Saros made 21 saves to lead the Predators to a 3–1 win over the Carolina Hurricanes and thus clinch their spot in the 2021 Stanley Cup Playoffs.

[97] On 30 November, Saros recorded his first shutout of the season as the Predators beat the Blue Jackets for the 40th time in franchise history.

[104] However, the Predators struggled to win games during this season and failed to qualify for the 2023 Stanley Cup playoffs for the first time in eight years.

[105] Following the departure of Rittich in the offseason, the Predators signed free agent Kevin Lankinen as Saros' backup netminder.

[107] After following this game up with a 38-save shutout on 9 January against the Ottawa Senators, Saros tied with Byron Dafoe for seventh place on the NHL's list of most saves by a goaltender in two consecutive starts.

[110] After failing to qualify for the playoffs, the Predators re-signed Lankinen as Saros' backup netminder[111] and also acquired various veteran players in the offseason including Ryan O'Reilly and Luke Schenn.