in 2011 Koskinen was drafted 31st overall by the
New York Islanders in the
2009 NHL entry draft after playing for the
Espoo Blues in the Finnish
SM-liiga. He was the first goalie and first Finnish player selected that year. Prior to the draft, he was the second-ranked European goaltender by
NHL Central Scouting Bureau. On 13 July 2009, Koskinen signed a three-year entry-level contract with the New York Islanders. In the
2009–10 season, his first in North America, Koskinen was assigned to the Islanders affiliate, the
Bridgeport Sound Tigers, to start the year. After only two appearances with the Sound Tigers, he suffered a torn
labrum in his hip which required surgery and ruled him out for the majority of the season. On 19 March 2010, after four months of rehab, Koskinen was reassigned to the secondary Islanders affiliate, the
Utah Grizzlies, for the remainder of the year. Undefeated in six starts, he helped the Grizzlies reach the conference semi-finals before returning to the Sound Tigers' first-round playoff series on 18 April 2010. Koskinen made his
National Hockey League (NHL) debut on 8 February 2011 against the
Toronto Maple Leafs as the Islanders lost 5–3. He earned his first career NHL win two days later in a 4–3 shootout victory over the
Montreal Canadiens. On 12 November 2011, Koskinen returned to Finland, signing with
KalPa. In April 2013, Koskinen signed with the
Espoo Blues. In September 2013, Koskinen left Finland to play for
Sibir Novosibirsk in the
Kontinental Hockey League (KHL). Part way through the 2014–15 season he was traded to
SKA Saint Petersburg for fellow goaltender
Alexander Salák. Koskinen and his team went on to win the
Gagarin Cup, the KHL championship trophy in April 2015 and 2017. On 1 May 2018, Koskinen agreed to terms on a one year, $2.5 million contract with the
Edmonton Oilers of the NHL. On 21 January 2019, the Oilers signed Koskinen to a three-year, $13.5 million extension. The decision to sign Koskinen for three years based on such a short tenure was considered unusual, and many speculated that it was a cause of the dismissal of controversial Oilers general manager
Peter Chiarelli days later. Koskinen made his postseason debut in the NHL with the Oilers on 1 August 2020, playing in relief of
Mike Smith in a 6–4 loss against the
Chicago Blackhawks in Game 1 of the qualifying round. He earned his first and only NHL playoff win of his career in Game 2, making 23 saves in a 6–3 win against the Blackhawks. After the end of the
2021–22 NHL season and the end of his contract with the Oilers, Koskinen signed a two-year contract with
HC Lugano of the Swiss
National League (NL) on 13 June 2022. On 3 April 2024, Koskinen announced his retirement from professional hockey after two seasons with Lugano. ==International play==