On 24th June 2019, Swiss international striker Josip Drmic signed for Norwich on a three year contract. He turned down an extension to his contract with Borussia Mönchengladbach and had been linked with Nuremberg, Turkish outfit Trabzonspor, Burnley, Bournemouth and Watford.

He was born in Switzerland to Croatian parents and holds dual nationality. He joined Zurich aged nine and rose through the youth and reserve team ranks before making his first team debut on 6th February 2010 against Neuchâtel Xamax, coming on as a substitute. He scored his first Swiss Super League goal in a 1–1 away draw against Luzern on 4th February 2012. During 2012/13, he scored 19 goals in 39 matches,

In July 2013, he moved to German side Nurnberg on a four year contract. In his first season, he finished third highest goalscorer in the Bundesliga with 17 goals.However Nurnberg were relegated and he signed for Bayer Leverkusen on 12th May 2014. he made 25 appearances, scoring six goals in his first season.

In June 2015, he moved to Borussia Monchengladbach. Struggling with injuries, he made just 41 league appearances scoring six goals and was loaned to Hamburg in 2016 (6 appearances, 1 goal).

He has played for Switzerland at Under-19, Under-21 and in the 2012 London Olympics before winning his first senior cap in September 2012 against Albania. His first international goal came in March 2014 against Croatia. He played for Switzerland in the 2014 World Cup in Brazil and in the 2018 World Cup in Russia (scoring against Costa Rica). At the time of his transfer to Norwich, he had 32 caps and 10 international goals.

Drmic made his Norwich debut on the opening day of the 2019/20 Premier League season as a late substitute in the 4-1 defeat at Liverpool. He scored his first Norwich goal as a consolation in Norwich's 5-1 thrashing by Aston Villa at Carrow Road on 7th October 2019.

Drmic made a total of 24 appearances during the 2019/20 season, scoring three goals as Norwich were relegated. His performances did no endear him to the Norwich fans and it appeared during July/August 2020 that Drmic would be finding a new club. Despite speculation linkin ghim with moves to Huddersfield and Birmingham during the October 2020 and January 2021 transfer windows, Drmic finally left City moving to Croatia to join HNK Rijeka on loan on 5th February 2021.

Drmic netted six goals in 16 appearances for Rijeka, with the striker discovering form towards the end of the season to help Rijeka qualify for the Europa League play-offs. City's loan export was even placed on the standby list for Switzerland's Euro 2020 squad. Croatian outlet Sportske Novosti reported on on 27th June 2021 that Rijeka are keen to bring Drmic back to Croatia and have expressed their interest to City but that the Canaries are holding out for a better offer. Drmic eventually returned to Rijeka on a season long loan on 6th July 2021 for the final 12 months of his City contract. He made 36 appearances during 2021/22 scoring 24 goals, finishing second hghest goalscorer as Rijeka finished fourth.

He was released by Norwich on 20th May 2022. On 10th June 2022 the Pink Un reported that Drmic had signed for Croatian champions Dinamo Zagreb on a three year contract. He said "I am extremely happy and proud of this moment. Dinamo is the Croatian champion, the best Croatian club, continuously wins trophies in domestic competitions and performs regularly in European competitions. I will personally do my best to thank the club for the trust they have gained in their field games and goals. I believe that Dinamo will continue with good results in the new season through the Super Cup match, then the championship and the Cup, and through the qualifications for the Champions League."