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 taken in the draft as well as the first Finnish player selected. 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 returned to health and 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 NHL debut on 8 February 2011 against the Toronto Maple Leafs. The Islanders were defeated 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 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 in the NHL, which was formalised 1 July 2018. On 21 January 2019, the Oilers signed Koskinen to a three-year, $13.5 million extension, carrying an annual cap hit of $4.5 million.
International play
Koskinen has represented Finland in the World Championships in 2014 and 2016. In 2016, he was included in the All-Star Team and was named the best goaltender.
