The Greece international, 23, spent last season on loan at the BayArena.
Papadopoulos has penned a five-year contract with Leverkusen.
"I am delighted that it worked out," he told the club's official website. "I am looking forward to my future with this great team and think we can still move forward a lot."
Papadopoulos leaves Schalke following a four-year spell at the Veltins-Arena.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Bayern MunichBayern | 6 | 4 | 2 | 0 | 20 | 7 | 13 | 14 |
| 2 | RB Leipzig | 6 | 4 | 2 | 0 | 9 | 2 | 7 | 14 |
| 3 | Eintracht FrankfurtFrankfurt | 6 | 4 | 1 | 1 | 14 | 9 | 5 | 13 |
| 4 | Freiburg | 6 | 4 | 0 | 2 | 9 | 7 | 2 | 12 |
| 5 | Bayer LeverkusenB. Leverkusen | 6 | 3 | 2 | 1 | 16 | 12 | 4 | 11 |
| 6 | Union BerlinUnion Berlin | 6 | 3 | 2 | 1 | 6 | 4 | 2 | 11 |
| 7 | Borussia DortmundDortmund | 6 | 3 | 1 | 2 | 12 | 11 | 1 | 10 |
| 8 | Stuttgart | 6 | 2 | 3 | 1 | 15 | 11 | 4 | 9 |
| 9 | Heidenheim | 6 | 3 | 0 | 3 | 10 | 8 | 2 | 9 |
| 10 | Mainz 05Mainz | 6 | 2 | 2 | 2 | 11 | 10 | 1 | 8 |
| 11 | Werder Bremen | 6 | 2 | 2 | 2 | 8 | 12 | -4 | 8 |
| 12 | Wolfsburg | 6 | 2 | 1 | 3 | 13 | 12 | 1 | 7 |
| 13 | Augsburg | 6 | 2 | 1 | 3 | 9 | 15 | -6 | 7 |
| 14 | Borussia MonchengladbachBorussia M'bach | 6 | 2 | 0 | 4 | 7 | 10 | -3 | 6 |
| 15 | St Pauli | 6 | 1 | 1 | 4 | 4 | 9 | -5 | 4 |
| 16 | Hoffenheim | 6 | 1 | 1 | 4 | 10 | 16 | -6 | 4 |
| 17 | Holstein Kiel | 6 | 0 | 2 | 4 | 9 | 19 | -10 | 2 |
| 18 | VfL BochumVfL Bochum | 6 | 0 | 1 | 5 | 6 | 14 | -8 | 1 |
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