The 28-year-old leaves Molineux after seven years in the Black Country for an undisclosed fee.
He has signed a three-year deal at Craven Cottage, and Fulham have the option to extend that by another year if they wish.
Stearman made 234 appearances and scored six goals since joining Wolves from Leicester City in 2007.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Liverpool | 14 | 11 | 2 | 1 | 29 | 11 | 18 | 35 |
| 2 | Chelsea | 15 | 9 | 4 | 2 | 35 | 18 | 17 | 31 |
| 3 | Arsenal | 15 | 8 | 5 | 2 | 29 | 15 | 14 | 29 |
| 4 | Manchester CityMan City | 15 | 8 | 3 | 4 | 27 | 21 | 6 | 27 |
| 5 | Nottingham ForestNott'm Forest | 15 | 7 | 4 | 4 | 19 | 18 | 1 | 25 |
| 6 | Aston Villa | 15 | 7 | 4 | 4 | 23 | 23 | 0 | 25 |
| 7 | Brighton & Hove AlbionBrighton | 15 | 6 | 6 | 3 | 25 | 22 | 3 | 24 |
| 8 | Bournemouth | 15 | 7 | 3 | 5 | 23 | 20 | 3 | 24 |
| 9 | Brentford | 15 | 7 | 2 | 6 | 31 | 28 | 3 | 23 |
| 10 | Fulham | 15 | 6 | 5 | 4 | 22 | 20 | 2 | 23 |
| 11 | Tottenham HotspurSpurs | 15 | 6 | 2 | 7 | 31 | 19 | 12 | 20 |
| 12 | Newcastle UnitedNewcastle | 15 | 5 | 5 | 5 | 19 | 21 | -2 | 20 |
| 13 | Manchester UnitedMan Utd | 15 | 5 | 4 | 6 | 19 | 18 | 1 | 19 |
| 14 | West Ham UnitedWest Ham | 15 | 5 | 3 | 7 | 20 | 28 | -8 | 18 |
| 15 | Everton | 14 | 3 | 5 | 6 | 14 | 21 | -7 | 14 |
| 16 | Leicester CityLeicester | 15 | 3 | 5 | 7 | 21 | 30 | -9 | 14 |
| 17 | Crystal Palace | 15 | 2 | 7 | 6 | 14 | 20 | -6 | 13 |
| 18 | Ipswich TownIpswich | 15 | 1 | 6 | 8 | 14 | 27 | -13 | 9 |
| 19 | Wolverhampton WanderersWolves | 15 | 2 | 3 | 10 | 23 | 38 | -15 | 9 |
| 20 | Southampton | 15 | 1 | 2 | 12 | 11 | 31 | -20 | 5 |
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