[1] Tarkki originally played professionally in his native Finland with Lukko, SaiPa and the Espoo Blues of the SM-liiga.

[2] On 6 May 2011, Tarkki signed as an undrafted free agent to a one-year entry-level contract with the Anaheim Ducks.

[3] Tarkki made his NHL debut for the Ducks on 8 January 2012, against the Columbus Blue Jackets, after primary goaltender Jonas Hiller was injured late in the first period.

[5][6] On 2 October 2013, he became free agent after cancellation of a contract with Salavat Yulaev Ufa of the Kontinental Hockey League (KHL).

[7] On 18 November 2013, he moved to the Swedish Hockey League, in agreeing to a contract for the remainder of the season with Linköpings HC.