The younger brother of Brentford defender Sepp van den Berg, Rav has moved to Germany in a permanent transfer.
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Rav was also being linked with Brentford, but has now joined FC Koln, penning a five-year contract.
Van den Berg missed the opening two games of Middlesbrough's new Championship campaign.
The 21-year-old Dutchman won Boro's player of the year award in the 2023-24 season and played in the Under-21 European Championships this summer.