Rice, who is retiring following Sunday's visit to West Bromwich Albion, has been involved at the Gunners for the past 44 years.
Current youth-team coach Bould, who made 372 appearances for the club as a player, was a key member of Wenger's double-winning team in 1998.
Meanwhile, reserve-team manager Neil Banfield will be promoted to first-team coach.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Manchester CityMan City | 37 | 27 | 7 | 3 | 93 | 33 | 60 | 88 |
| 2 | Arsenal | 37 | 27 | 5 | 5 | 89 | 28 | 61 | 86 |
| 3 | Liverpool | 37 | 23 | 10 | 4 | 84 | 41 | 43 | 79 |
| 4 | Aston Villa | 37 | 20 | 8 | 9 | 76 | 56 | 20 | 68 |
| 5 | Tottenham HotspurSpurs | 37 | 19 | 6 | 12 | 71 | 61 | 10 | 63 |
| 6 | Chelsea | 37 | 17 | 9 | 11 | 75 | 62 | 13 | 60 |
| 7 | Newcastle UnitedNewcastle | 37 | 17 | 6 | 14 | 81 | 60 | 21 | 57 |
| 8 | Manchester UnitedMan Utd | 37 | 17 | 6 | 14 | 55 | 58 | -3 | 57 |
| 9 | West Ham UnitedWest Ham | 37 | 14 | 10 | 13 | 59 | 71 | -12 | 52 |
| 10 | Brighton & Hove AlbionBrighton | 37 | 12 | 12 | 13 | 55 | 60 | -5 | 48 |
| 11 | Bournemouth | 37 | 13 | 9 | 15 | 53 | 65 | -12 | 48 |
| 12 | Crystal Palace | 37 | 12 | 10 | 15 | 52 | 58 | -6 | 46 |
| 13 | Wolverhampton WanderersWolves | 37 | 13 | 7 | 17 | 50 | 63 | -13 | 46 |
| 14 | Fulham | 37 | 12 | 8 | 17 | 51 | 59 | -8 | 44 |
| 15 | Everton | 37 | 13 | 9 | 15 | 39 | 49 | -10 | 40 |
| 16 | Brentford | 37 | 10 | 9 | 18 | 54 | 61 | -7 | 39 |
| 17 | Nottingham ForestNott'm Forest | 37 | 8 | 9 | 20 | 47 | 66 | -19 | 29 |
| 18 | Luton TownLuton | 37 | 6 | 8 | 23 | 50 | 81 | -31 | 26 |
| R | Burnley | 37 | 5 | 9 | 23 | 40 | 76 | -36 | 24 |
| R | Sheffield UnitedSheff Utd | 37 | 3 | 7 | 27 | 35 | 101 | -66 | 16 |
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