Reus has been skippering the side since the 2018/2019 season.
He recently signed a new contract that will last until the summer of 2024, extending his stay at the club into a 12th campaign.
Reus suffered fitness issues last season and missed the 2022 FIFA World Cup in Qatar.
The 34-year-old Germany international has made 387 appearances and scored 161 goals since signing for Dortmund from Borussia Monchengladbach in the summer of 2012.
He is just 16 goals behind the club's record goalscorer Adi Preissler.
'Hello dear BVB fans,' a video of the now-former skipper began in the video posted to the club's official Twitter account.
'It's very important for me to tell you something personally: I had a lot of time to think during my vacation and decided to pass on the captain's armband.
'I informed Edin Terzic and Sebastian Kehl about this yesterday. I was allowed to wear this armband for five years with pride and honour.
'Thank you for your support over the years and I wish Edin and Sebastian that they find a very good successor - I am sure that they will be successful.'
Reus has won two DFB-Pokals and two German Super Cups during his time at Dortmund.
