The Belgian, 23, has penned a three-and-a-half-year deal with the Championship club.
Vermijl was expected to join Wednesday on loan, but he has instead moved to Hillsborough permanently.
He will wear shirt number 36 for the Owls.
Vermijl leaves United following nearly five years at Old Trafford as both a youth player and a member of the senior squad.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| C | Manchester CityMan City | 38 | 28 | 7 | 3 | 96 | 34 | 62 | 91 |
| 2 | Arsenal | 38 | 28 | 5 | 5 | 91 | 29 | 62 | 89 |
| 3 | Liverpool | 38 | 24 | 10 | 4 | 86 | 41 | 45 | 82 |
| 4 | Aston Villa | 38 | 20 | 8 | 10 | 76 | 61 | 15 | 68 |
| 5 | Tottenham HotspurSpurs | 38 | 20 | 6 | 12 | 74 | 61 | 13 | 66 |
| 6 | Chelsea | 38 | 18 | 9 | 11 | 77 | 63 | 14 | 63 |
| 7 | Newcastle UnitedNewcastle | 38 | 18 | 6 | 14 | 85 | 62 | 23 | 60 |
| 8 | Manchester UnitedMan Utd | 38 | 18 | 6 | 14 | 57 | 58 | -1 | 60 |
| 9 | West Ham UnitedWest Ham | 38 | 14 | 10 | 14 | 60 | 74 | -14 | 52 |
| 10 | Crystal Palace | 38 | 13 | 10 | 15 | 57 | 58 | -1 | 49 |
| 11 | Brighton & Hove AlbionBrighton | 38 | 12 | 12 | 14 | 55 | 62 | -7 | 48 |
| 12 | Bournemouth | 38 | 13 | 9 | 16 | 54 | 67 | -13 | 48 |
| 13 | Fulham | 38 | 13 | 8 | 17 | 55 | 61 | -6 | 47 |
| 14 | Wolverhampton WanderersWolves | 38 | 13 | 7 | 18 | 50 | 65 | -15 | 46 |
| 15 | Everton | 38 | 13 | 9 | 16 | 40 | 51 | -11 | 40 |
| 16 | Brentford | 38 | 10 | 9 | 19 | 56 | 65 | -9 | 39 |
| 17 | Nottingham ForestNott'm Forest | 38 | 9 | 9 | 20 | 49 | 67 | -18 | 32 |
| R | Luton TownLuton | 38 | 6 | 8 | 24 | 52 | 85 | -33 | 26 |
| R | Burnley | 38 | 5 | 9 | 24 | 41 | 78 | -37 | 24 |
| R | Sheffield UnitedSheff Utd | 38 | 3 | 7 | 28 | 35 | 104 | -69 | 16 |
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