The midfielder has signed a long-term deal with Dortmund, who are known for signing youngsters.
"I would like to say that I am grateful to have been given this opportunity," Matthews told SABCSport.
The Cape Town-born player, who has been training with the Dortmund-based side since July 2018, is excited to have joined one of the biggest clubs in Europe.
"I am really excited to have joined one of Europe's biggest football clubs. I am excited to get going," he added.
Matthews became a free agent after leaving Ajax at the end of last season with the Mother City-based side having been relegated to the National First Division (NFD) from the PSL.
Dortmund had to wait until Matthews was 18 before offering him a professional contract.
The teenager has since joined the club following in the footsteps of his compatriots Marc Arnold, Delron Buckley and Steven Pienaar, who were once on the books of Dortmund.
Matthews took to Instagram to express further delight at signing for Dortmund.