The European club unveiled the new acquisition on Friday, revealing that the 23-year-old had penned a two-year contract until 2028 with the option of an additional year.
Reid made the announcement on its club website and social media, admitting that the youngster serves as a replacement for Antonio van Wyk who recently left the club to join Mamelodi Sundowns.
"After the departure of Antonio van Wyk, we were looking for a player who covered Toni's strengths and was also a little more determined towards the opponent's goal," read the statement.
"Since we have good experience with South African players, the market was of course interesting for us. Jaedin is a direct player who is very good at pressing and has a good feeling for depth.
"We are very pleased that he has decided to join SV Oberbank Ried, although he had some other offers."
Rhodes was also heavily linked with a move to Masandawana as well but has opted for greener pastures abroad after making 93 top-flight appearances for City, scoring nine goals while providing four assists.
"I chose SV Oberbank Ried because it has always been my dream to play in Europe," said Rhodes.
"And I know that Ried is now the perfect club for me. My goal is to learn as much as possible and to write a piece of history with the club.
"Austrian football is fast-paced and very physical. My strengths lie in pressing and transition play – that's exactly what Austrian football is all about."
He becomes the third South African footballer to join the club after van Wyk and Yusuf Maart.