The 28-year-old, who has left the Premier League club for an undisclosed fee, moves to Ewood Park on a two-and-a-half-year deal.
The Scotland international has spent the majority of the campaign on loan at Brighton & Hove Albion, where he scored one goal in 13 appearances.
Conway is expected to feature in the Blackburn squad for Saturday's game with Blackpool.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Sunderland | 15 | 9 | 4 | 2 | 25 | 11 | 14 | 31 |
| 2 | Sheffield UnitedSheff Utd | 15 | 10 | 3 | 2 | 19 | 7 | 12 | 31 |
| 3 | Leeds UnitedLeeds | 15 | 8 | 5 | 2 | 24 | 9 | 15 | 29 |
| 4 | Burnley | 15 | 7 | 6 | 2 | 18 | 6 | 12 | 27 |
| 5 | West Bromwich AlbionWest Brom | 15 | 6 | 7 | 2 | 16 | 9 | 7 | 25 |
| 6 | Watford | 15 | 8 | 1 | 6 | 23 | 22 | 1 | 25 |
| 7 | Middlesbrough | 15 | 7 | 3 | 5 | 23 | 17 | 6 | 24 |
| 8 | Millwall | 15 | 6 | 5 | 4 | 18 | 13 | 5 | 23 |
| 9 | Blackburn RoversBlackburn | 15 | 6 | 4 | 5 | 19 | 17 | 2 | 22 |
| 10 | Bristol City | 15 | 5 | 7 | 3 | 20 | 19 | 1 | 22 |
| 11 | Swansea CitySwansea | 15 | 5 | 4 | 6 | 11 | 10 | 1 | 19 |
| 12 | Derby CountyDerby | 15 | 5 | 4 | 6 | 19 | 19 | 0 | 19 |
| 13 | Stoke CityStoke | 15 | 5 | 4 | 6 | 18 | 19 | -1 | 19 |
| 14 | Norwich CityNorwich | 15 | 4 | 6 | 5 | 23 | 22 | 1 | 18 |
| 15 | Sheffield WednesdaySheff Weds | 15 | 5 | 3 | 7 | 17 | 25 | -8 | 18 |
| 16 | Oxford UnitedOxford Utd | 15 | 4 | 5 | 6 | 17 | 18 | -1 | 17 |
| 17 | Coventry CityCoventry | 15 | 4 | 4 | 7 | 20 | 21 | -1 | 16 |
| 18 | Plymouth ArgylePlymouth | 15 | 4 | 4 | 7 | 15 | 26 | -11 | 16 |
| 19 | Hull City | 15 | 3 | 6 | 6 | 16 | 20 | -4 | 15 |
| 20 | Preston North EndPreston | 15 | 3 | 6 | 6 | 15 | 23 | -8 | 15 |
| 21 | Luton TownLuton | 15 | 4 | 3 | 8 | 17 | 26 | -9 | 15 |
| 22 | Cardiff CityCardiff | 15 | 4 | 3 | 8 | 14 | 23 | -9 | 15 |
| 23 | Portsmouth | 15 | 2 | 6 | 7 | 16 | 28 | -12 | 12 |
| 24 | Queens Park RangersQPR | 15 | 1 | 7 | 7 | 12 | 25 | -13 | 10 |
| > Championship Full Table | |||||||||
