The 22-year-old keeper had been looking for a new club after his release from Rovers at the end of last season.
"It's good to get things done as it's been a long summer," Woods told Watford's official website. "I felt this move was right for me and hopefully I can kick on."
Woods began his career with Manchester United before joining Doncaster in 2009.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Leicester CityLeicester | 44 | 30 | 4 | 10 | 86 | 39 | 47 | 94 |
| 2 | Leeds UnitedLeeds | 44 | 27 | 9 | 8 | 80 | 37 | 43 | 90 |
| 3 | Ipswich TownIpswich | 43 | 26 | 11 | 6 | 85 | 53 | 32 | 89 |
| 4 | Southampton | 44 | 25 | 9 | 10 | 85 | 61 | 24 | 84 |
| 5 | West Bromwich AlbionWest Brom | 44 | 20 | 12 | 12 | 67 | 44 | 23 | 72 |
| 6 | Norwich CityNorwich | 44 | 21 | 9 | 14 | 77 | 61 | 16 | 72 |
| 7 | Hull City | 44 | 19 | 12 | 13 | 65 | 56 | 9 | 69 |
| 8 | Coventry CityCoventry | 43 | 17 | 12 | 14 | 68 | 55 | 13 | 63 |
| 9 | Middlesbrough | 44 | 18 | 9 | 17 | 64 | 60 | 4 | 63 |
| 10 | Preston North EndPreston | 44 | 18 | 9 | 17 | 56 | 61 | -5 | 63 |
| 11 | Cardiff CityCardiff | 44 | 19 | 5 | 20 | 50 | 61 | -11 | 62 |
| 12 | Bristol City | 44 | 16 | 11 | 17 | 51 | 47 | 4 | 59 |
| 13 | Sunderland | 44 | 16 | 8 | 20 | 52 | 51 | 1 | 56 |
| 14 | Swansea CitySwansea | 44 | 15 | 11 | 18 | 57 | 62 | -5 | 56 |
| 15 | Watford | 44 | 12 | 17 | 15 | 59 | 58 | 1 | 53 |
| 16 | Millwall | 44 | 14 | 11 | 19 | 43 | 55 | -12 | 53 |
| 17 | Stoke CityStoke | 44 | 13 | 11 | 20 | 44 | 60 | -16 | 50 |
| 18 | Queens Park RangersQPR | 44 | 13 | 11 | 20 | 41 | 57 | -16 | 50 |
| 19 | Blackburn RoversBlackburn | 44 | 13 | 10 | 21 | 58 | 74 | -16 | 49 |
| 20 | Plymouth ArgylePlymouth | 44 | 12 | 12 | 20 | 58 | 69 | -11 | 48 |
| 21 | Sheffield WednesdaySheff Weds | 44 | 13 | 8 | 23 | 39 | 68 | -29 | 47 |
| 22 | Birmingham CityBirmingham | 44 | 12 | 10 | 22 | 48 | 64 | -16 | 46 |
| 23 | Huddersfield TownHuddersfield | 44 | 9 | 17 | 18 | 47 | 74 | -27 | 44 |
| R | Rotherham UnitedRotherham | 44 | 4 | 12 | 28 | 32 | 85 | -53 | 24 |
| > Championship Full Table | |||||||||
