In January 2014, Brandt moved to Bayer Leverkusen during the January transfer window for a fee of €350,000, where he signed a professional contract until 2019. He made his professional debut on 15 February 2014 in the Bundesliga against Schalke 04. He replaced Son Heung-min after 82 minutes in a 1–2 home defeat. Three days later he made his debut in the European Cup when he came on in the first knockout round first leg against Paris Saint-Germain in the UEFA Champions League. On 4 April 2014, he scored his first goal for Bayer Leverkusen, as he made it 1–1 in the 1–2 defeat against Hamburger SV.

On 15 August 2015, Brandt scored the winning goal after appearing as a substitute in a 2–1 defeat of 1899 Hoffenheim in Bayer’s opening match of the 2015–16 Bundesliga season. Between 20 March and 30 April 2016, he scored in six consecutive Bundesliga matches, becoming the youngest player since Gerd Müller to achieve this by scoring 72 seconds into a 2–1 home win over Hertha BSC.

On 17 May 2016, Brandt was named in Germany’s preliminary 27-man squad for UEFA Euro 2016.

On 26 August 2017, Brandt became the youngest-ever Leverkusen player to reach 100 Bundesliga appearance, doing so at the age 21 years, three months and 25 days during a 2–2 draw against Hoffenheim.

On 4 June 2018, Brandt was included in Germany’s final 23-man squad for the 2018 FIFA World Cup. On 17 June, Brandt made his first World Cup appearance as a substitute by replacing Timo Werner in the 86th minute in the opening match against Mexico in which they lost 1–0.

During the second half of the 2018–19 Bundesliga campaign, Brandt was re-positioned by new club manager Peter Bosz, shifting from his natural wide position to a more central role in midfield alongside Kai Havertz. His goal contribution increased as a result of the positional change and in February 2019, after scoring twice and assisting a further four goals, he was nominated for the Player of the Month award. He ultimately won the award and in doing so became the first Leverkusen player to claim the accolade. His brace against Mainz 05 at the start of the month also came on the occasion of his 200th appearance for the club across all competitions.

Brandt was Dortmund’s transfer target after the 23-year-old scored seven league goals, provided eleven assists and subsequently helped Leverkusen to finish fourth in Bundesliga and secure a Champions League third qualifying round spot for next season. On 22 May 2019, Brandt completed a transfer to Borussia Dortmund on a five-year deal for a reported €25 million after Dortmund activated a release clause in his contract. He arrived at the same time as new teammate Thorgan Hazard, who moved from Borussia Mönchengladbach.