| Season Review | Matches: 1959 – 1960 | 1959-1960 Pictures |
Appearances (Goals in brackets)
* – left Celtic during season 1959/60
† – left Celtic at the end of season 1959/60
| League | League Cup | Scottish Cup | Total | |
| Haffey | 20 | 6 | 7 | 33 |
| Fallon | 14 | 0 | 0 | 14 |
| Donnelly | 5 | 0 | 0 | 5 |
| Kennedy | 20 | 3 | 7 | 30 |
| Curran | 3 | 0 | 0 | 3 |
| Mochan | 29 (13) | 3 (1) | 7 (8) | 39 (22) |
| MacKay | 29 | 6 | 7 | 42 |
| Smith † | 21 | 3 | 5 (2) | 29 (2) |
| Clark | 2 | 0 | 0 | 2 |
| Evans † | 30 | 6 | 7 | 43 |
| McNeill | 19 | 6 | 7 | 32 |
| Kurila | 1 | 0 | 0 | 1 |
| Peacock | 33 (2) | 4 | 7 | 44 (2) |
| Crerand | 8 (1) | 0 | 0 | 8 (1) |
| Carroll | 10 (1) | 2 (1) | 0 | 12 (2) |
| Slater | 1 | 0 | 0 | 1 |
| McVittie * | 1 | 5 | 0 | 6 |
| Colrain | 15 (5) | 3 | 7 (1) | 25 (6) |
| Chalmers | 17 (14) | 0 | 2 (1) | 19 (15) |
| O'Hara | 6 (1) | 2 | 0 | 8 (1) |
| Gallacher | 4 | 1 | 0 | 5 |
| Jackson | 12 (8) | 2 (2) | 1 | 15 (10) |
| Conway | 12 (6) | 2 | 0 | 14 (6) |
| Lochhead | 1 | 1 | 0 | 2 |
| Divers | 24 (12) | 3 (1) | 7 (3) | 34 (16) |
| Auld | 20 (3) | 3 (1) | 1 | 24 (4) |
| Byrne | 14 (4) | 3 | 5 (1) | 22 (5) |
| Mackle | 3 (1) | 2 (1) | 0 | 5 (2) |