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 with 32 goals in 34 games, 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.
Dost played for the Netherlands at under-20 and under-21 level. He was called up to the senior side for the first time in August 2012, but did not make his debut until March 2015.
Born in Deventer, Dost's first club was CVV Germanicus in Coevorden, where he spent his youth career. After a few seasons, FC Emmen took Dost into their youth academy.
Dost showed his potential at Emmen and the club offered him a contract before the start of the 2007–08 season, during which he played for the main squad. He started as on the bench, but later on in the season he was given more time to play. At one point he was just about to move to Finland, to RoPS as Emmen's former technical director Tom Saintfiet was coaching there. The move was turned down by RoPS's management. Dost scored his first goal for Emmen on 18 February 2008 in the game against Fortuna Sittard. Among later goals, the most notable were a hat trick in the Derby match against BV Veendam, which Emmen won 3–2.
Dost moved to Heracles Almelo in the summer of 2008, for a transfer fee of more than €300,000. Dost showed his potential and was considered one of the Eredivisie's best talents. After this successful season there were many rumours that Dost would be transferred to Ajax. These rumours didn't eventuate because he signed for SC Heerenveen on 4 February 2010 on the advice of agent Henk Nienhuis.
On 18 May 2010, Dost was signed by SC Heerenveen. The 20-year-old arrived from Heracles Almelo for a transfer fee of around €3.2 million, on a five-year-deal. In his first season with the Heerenveen, he finished as the club's top scorer with 13 league goals.
On 10 December 2011, Dost scored all five goals in Heerenveen's 5–0 win away to SBV Excelsior, taking his total to 14 goals in 16 Eredivisie games. He finished as the topscorer in the Eredivisie with 32 league goals in 34 matches.
On 1 June 2012, it was announced by the official website of VfL Wolfsburg that Dost would join the club. On 25 August 2012, he scored the winner away against VfB Stuttgart on his Bundesliga debut. Following the sacking of Felix Magath, Dost scored a brace in Lorenz-Günther Köstner's debut as manager, a 4–1 thumping of Fortuna Düsseldorf on 27 October. After the appointment of Klaus Allofs as sporting director, Dost netted Wolfsburg's second, and the eventual winner, in a 3–1 defeat of Hoffenheim on 18 November, lifting die Wölfe out of the bottom three.
On 8 December 2013, he scored the winning goal against champions Borussia Dortmund to secure a 3–2 away victory.
Dost started the 2014–15 season as Wolfsburg's third choice striker and made his European debut on matchday three of the Europa League in a 4–2 win against FC Krasnodar.
On 30 January 2015, he scored two goals in a 4–1 home win against Bayern Munich in the Bundesliga, the first player in 102 games to do so against that opponent. On 14 February, he scored four goals, away from home against Bayer Leverkusen in a 5–4 win, to bring his tally to nine goals in 10 Bundesliga matches, and five days later, Dost scored two goals in a 2–0 win against Sporting CP in the first knockout round of the Europa League. On 22 February, he scored twice in a 2–1 win against Hertha BSC, to bring his total to eight goals in three matches in a one-week period. Dost's form continued with two goals in Wolfsburg's 5–3 defeat of SV Werder Bremen on 1 March to bring his tally to 11 goals in six Bundesliga matches in 2015.
On 30 May, Dost headed in the final goal from an Ivan Perišić cross as Wolfsburg won their first DFB-Pokal with a 3–1 triumph over Borussia Dortmund at the Olympiastadion. He was the most efficient striker in Europe that season, scoring 18 goals from 54 shots.
On 13 January 2016, Dost suffered a broken foot after Dante injured him in training.
On 28 August 2016, Sporting CP announced that they had signed Dost for €10 million, potentially rising to €12 million, and a buyout clause of €60 million. He made his debut on 10 September at home to Moreirense F.C., concluding a 3–0 win; thirteen days later he scored for the third successive game, netting twice in a 4–2 victory over G.D. Estoril Praia again at the Estádio José Alvalade.
Dost scored all of Sporting's goals on 11 March 2017 as they won 4–1 at C.D. Tondela; two were penalties, of which he later missed another. On 9 April, he scored another hat-trick in a 4–0 home win over Boavista FC, and three weeks later another treble won the game 3–2 at S.C. Braga. He ended up scoring more goals than games played in the league, hitting the net amazingly 34 times in 31 games.
In August 2012, he was called up by new manager Louis van Gaal for a friendly match in the King Baudouin Stadium in Brussels against Belgium but did not feature. He returned to the squad in March 2015 after a spell of good form for Wolfsburg, being named in Guus Hiddink's squad for a European qualifier against Turkey, and a friendly against Spain. He made his debut in the first match on 28 March at the Amsterdam ArenA, replacing defensive midfielder Nigel de Jong after 63 minutes as the Netherlands equalised for a 1–1 draw. On 13 November, away to Wales at the Cardiff City Stadium, he headed his first international goal to open a 3–2 win.As of 23 August 2017
As of 4 June 2017
Score and result list Netherlands' goal tally first.
Eredivisie Top Scorer: 2011–12
KNVB Cup Top Scorer: 2011–12
Primeira Liga Top Scorer: 2016–17