The 37-year-old joined the club from West Bromwich Albion in 2003 and has made 307 appearances for the Clarets.
Burnley boss Eddie Howe told the club's official website: "We always wanted him as part of the squad and his experience will be vital."
Jensen made just four league appearances last season.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Leeds UnitedLeeds | 26 | 15 | 8 | 3 | 48 | 19 | 29 | 53 |
| 2 | Burnley | 26 | 14 | 10 | 2 | 31 | 9 | 22 | 52 |
| 3 | Sheffield UnitedSheff Utd | 26 | 16 | 6 | 4 | 36 | 17 | 19 | 52 |
| 4 | Sunderland | 26 | 14 | 8 | 4 | 39 | 22 | 17 | 50 |
| 5 | Middlesbrough | 26 | 11 | 8 | 7 | 43 | 32 | 11 | 41 |
| 6 | West Bromwich AlbionWest Brom | 26 | 9 | 13 | 4 | 32 | 21 | 11 | 40 |
| 7 | Blackburn RoversBlackburn | 25 | 11 | 6 | 8 | 28 | 23 | 5 | 39 |
| 8 | Watford | 26 | 11 | 5 | 10 | 36 | 37 | -1 | 38 |
| 9 | Bristol City | 26 | 9 | 10 | 7 | 33 | 30 | 3 | 37 |
| 10 | Sheffield WednesdaySheff Weds | 26 | 10 | 7 | 9 | 38 | 40 | -2 | 37 |
| 11 | Norwich CityNorwich | 26 | 9 | 9 | 8 | 43 | 37 | 6 | 36 |
| 12 | Swansea CitySwansea | 26 | 9 | 7 | 10 | 30 | 30 | 0 | 34 |
| 13 | Queens Park RangersQPR | 26 | 7 | 11 | 8 | 29 | 34 | -5 | 32 |
| 14 | Millwall | 25 | 7 | 9 | 9 | 24 | 23 | 1 | 30 |
| 15 | Preston North EndPreston | 26 | 6 | 12 | 8 | 28 | 34 | -6 | 30 |
| 16 | Coventry CityCoventry | 26 | 7 | 8 | 11 | 34 | 37 | -3 | 29 |
| 17 | Oxford UnitedOxford Utd | 26 | 7 | 8 | 11 | 29 | 41 | -12 | 29 |
| 18 | Derby CountyDerby | 26 | 7 | 6 | 13 | 31 | 35 | -4 | 27 |
| 19 | Stoke CityStoke | 26 | 6 | 9 | 11 | 24 | 32 | -8 | 27 |
| 20 | Luton TownLuton | 26 | 7 | 4 | 15 | 27 | 44 | -17 | 25 |
| 21 | Cardiff CityCardiff | 26 | 5 | 9 | 12 | 26 | 41 | -15 | 24 |
| 22 | Portsmouth | 24 | 5 | 8 | 11 | 30 | 41 | -11 | 23 |
| 23 | Hull City | 26 | 5 | 8 | 13 | 25 | 36 | -11 | 23 |
| 24 | Plymouth ArgylePlymouth | 26 | 4 | 9 | 13 | 25 | 54 | -29 | 21 |
| > Championship Full Table | |||||||||
