The 21-year-old yesterday put pen to paper on a four-year deal with Hamburg after the Bundesliga side took advantage of the player’s expiring contract.
The centre-back has generally impressed in his 17 appearances this term, including a man of the match award the last time Rangers travelled to Celtic Park.
However, Ibrox chiefs believed he wasn’t worth his demands of a new deal and talks broke down in March.
Bates joined the club at the beginning of the 2016/17 Scottish Premiership season on loan from then-Championship club Raith Rovers. That move was made permanent in January the following year.