The 24-year-old has penned a four-year deal with Marcelo Bielsa’s side and leaves Freiburg after three seasons.
The two clubs did not disclose a fee but reports state that Leeds are paying around £13m (€14.6m) for Koch.
✍️ #LUFC are pleased to announce the signing of Robin Koch from Bundesliga side SC Freiburg
— Leeds United (@LUFC) August 29, 2020
Bielsa turned to Koch after Brighton refused to negotiate the sale of Ben White to Leeds.
Koch won his first two caps for Germany last year and is in their latest squad for games against Spain and Switzerland.
The defender leaves Freiburg for Leeds after making 87 appearances and scoring give goals.
He is Leeds’ second big signing of the week after they earlier broke their club record to sign Rodrigo Moreno from Valencia.