| Season Review | Matches: 1962 – 1963 | 1962-1963 Pictures |
Appearances (Goals in brackets)
* – left Celtic during season 1962/63
† – left Celtic at the end of season 1962/63
| League | League Cup | Scottish Cup | Fairs Cup | Total | |
| Haffey | 33 | 6 | 7 | 1 | 47 |
| Fallon | 0 | 0 | 0 | 1 | 1 |
| Madden | 1 | 0 | 0 | 0 | 1 |
| MacKay | 29 (4) | 6 | 6 (2) | 2 | 43 (6) |
| Young | 5 | 0 | 1 | 0 | 6 |
| Kennedy | 25 | 6 | 5 | 1 | 37 |
| Gemmell | 2 | 0 | 1 | 0 | 3 |
| Crerand * | 17 | 6 (1) | 0 | 2 (1) | 25 (2) |
| McNeill | 28 (1) | 6 | 7 | 1 | 42 (1) |
| Cushley | 2 | 0 | 0 | 0 | 2 |
| McCarron | 1 | 0 | 0 | 0 | 1 |
| Price | 27 (3) | 6 | 7 | 0 | 40 (3) |
| Clark | 2 | 0 | 0 | 1 | 3 |
| O'Neill | 13 | 0 | 1 | 2 | 16 |
| McNamee | 19 (2) | 0 | 7 (1) | 1 | 27 (3) |
| Johnstone | 4 (1) | 0 | 1 | 0 | 5 (1) |
| Lennox | 4 | 5 | 0 | 0 | 9 |
| Craig | 17 (13) | 0 | 3 | 1 | 21 (13) |
| Chalmers | 27 (11) | 1 | 4 (1) | 2 | 34 (12) |
| Gallacher | 17 (3) | 6 (3) | 3 (1) | 2 | 28 (7) |
| Carroll * | 6 (2) | 0 | 0 | 1 (1) | 7 (3) |
| Murdoch | 19 (4) | 6 (2) | 6 (5) | 0 | 31 (11) |
| Hughes | 16 (11) | 6 (6) | 6 (4) | 0 | 28 (21) |
| Jackson * | 2 (1) | 0 | 0 | 1 | 3 (1) |
| Divers | 27 (11) | 0 | 7 (2) | 1 | 35 (13) |
| Byrne† | 9 (1) | 6 | 0 | 2 | 17 (1) |
| Brogan | 18 (4) | 0 | 5 (2) | 0 | 23 (6) |
| Jeffrey | 4 | 0 | 0 | 0 | 4 |
| own goals | (4) | (2) | (6) |