Having begun his career at FC Emmen in the Eerste Divisie, Dost later played in the Eredivisie for Heracles Almelo and SC Heerenveen. In 2012, after being the top scorer in the league, he was signed by VfL Wolfsburg. Four years later, having helped his team win the DFB-Pokal he signed for Primeira Liga side Sporting CP. He won the Bola de Prata for top scorer in his first Primeira Liga season, with 34 goals in 31 games. At Sporting, Dost won the Taça de Portugal once and the Taça da Liga twice. Currently plays for Bundesliga club Eintracht Frankfurt.