Hamburg’s scouting directory Johannes Spors said: “David will bring physicality, speed, a good mentality and leadership to our defence; qualities that will certainly help.
“He is a down-to-earth guy who is actively looking to develop his career and is willing to work hard for it.”
Bates joined Rangers initially on loan from Raith Rovers in 2016.
He signed permanently at the end of that season and has made 19 appearances in light blue.
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