The 32-year-old goalkeeper has been under contract with Borussia Dortmund since July 2022. He previously played for Jahn Regensburg and has made 12 appearances for BVB across all competitions as of June 2023 (all figures are accurate as of that date).

He played his first Champions League game before his first Bundesliga match. Meyer was between the sticks more often than expected in his debut season for the Black and Yellows: seven times in the league, five times in the Champions League. "Alex is much more than a back-up goalkeeper. Whenever he was needed, he showed his abilities at an extraordinarily high level. He is a model team player, a great footballer and a very reliable professional with real life experience, who gives the team a sense of calm and security," said sporting director Sebastian Kehl as he offered the 32-year-old a new contract well before his previous deal was due to expire. Meyer signed in July 2023, extending his stay at BVB until 2025. "I know my role and I know what I'm going to do here. Nevertheless, I always try to give it my all. I have a good relationship with Gregor [Kobel], try to support him and want to be there in case something happens. Then I want to show that I can be relied upon. With the fans, and this all has a completely different meaning here than at my previous clubs, but I enjoy it when you can see that no matter where we are, the Dortmund fans are also there for us. That makes me proud," he said in an interview with bvb.de.

Alexander Meyer grew up 50 kilometres north of Hamburg and was an HSV supporter from birth. On his 14th birthday, his dream came true when he was invited to a trial training session at his favourite team. He clearly made a good impression and soon joined the Hamburg club as an U15 for the 2005/06 season, moving from local side VfL Oldesloe. From January 2009 onward, he no longer threw balls to the first team players from the sidelines of the Volksparkstadion as a ball boy, but rather saved their shots as he was called up to take part in the squad's winter training camp in Dubai.

Less than six months later, he suffered a serious setback when he was sidelined for over a year due to a shoulder injury. The club had signed a replacement in the meantime, meaning that Meyer, in his first two seasons at senior level, only made ten appearances for HSV's U23 team in the Regionalliga Nord from October 2010 to April 2012. "I probably would have got my first pro contract at HSV if I hadn't injured my shoulder so badly," Meyer later told Goalguard.

After seven years at HSV, the 1.95-metre tall goalkeeper stayed in the fourth tier when he moved to TSV Havelse for the 2012/13 season. However, he also had to battle adversity at his new club after a solid start which saw him appear in the first 13 games of the season. First came another shoulder injury, then a cruciate ligament rupture meant that he only managed to play one game from November 2012 to April 2014. In 2014/15, Meyer was finally injury free, appearing in 33 of 34 games that season. In 2016, he left Havelse after 93 Regionalliga appearances to join Energie Cottbus, where he immediately became the number one goalkeeper, but again suffered a serious injury which meant he missed six months of action. 

On 13 August 2017, Energie Cottbus faced VfB Stuttgart in the DFB-Pokal. Although the former Bundesliga club ultimately lost in a penalty shoot-out, they had Meyer's many saves (including a penalty) to thank for getting there in the first place. Although the former Bundesliga club ultimately lost in a penalty shoot-out, they had Meyer's many saves (including a penalty) to thank for getting there in the first place. Unfortunately, injuries continued to plague him:  in July 2018, he tore his cruciate ligament in training. At the end of the season, Stuttgart were relegated from the Bundesliga and parted ways with their second-choice keeper

Despite his multiple battles with injury, Meyer has developed an excellent reputation as a goalkeeper. He exudes calmness while also being able to trouble opposing strikers with his physicality and presence. In his three seasons at Jahn Regensburg, he made 94 Bundesliga 2 appearances – only Heidenheim's Kevin Müller made more in the same timeframe (100 matchdays) – and conceded just 135 goals, one every 68 minutes. In the 2020/21 season, he saved 74% of opponents' shots on goal, compared to 69% in the previous season. He also earned the reputation of the "penalty killer". Out of eleven penalty kicks conceded by Regensburg, only six were converted, with Meyer making three saves. "He took his skills of anticipation to new levels in 2020/21. In the cup, Jahn won three consecutive games on penalties, with Meyer saving five in the process," reported the portal Spox.