The 20-year-old, who can operate as an attacking midfielder or striker, pens a three-year deal at St Andrew's.
Adams made 54 appearances for the Blades, scoring 15 goals, after joining from Ilkeston Town in 2014.
Birmingham had previously seen offers reportedly worth £1.2m and £1.7m rejected by Bramall Lane's board of directors.
Restore Data
| Team | P | W | D | L | F | A | GD | PTS | |
| 1 | Birmingham CityBirmingham | 24 | 17 | 5 | 2 | 42 | 17 | 25 | 56 |
| 2 | Wycombe WanderersWycombe | 26 | 16 | 6 | 4 | 52 | 28 | 24 | 54 |
| 3 | Wrexham | 26 | 15 | 6 | 5 | 38 | 20 | 18 | 51 |
| 4 | Huddersfield TownHuddersfield | 25 | 14 | 6 | 5 | 39 | 21 | 18 | 48 |
| 5 | Barnsley | 26 | 12 | 6 | 8 | 40 | 36 | 4 | 42 |
| 6 | Stockport CountyStockport | 26 | 11 | 8 | 7 | 40 | 28 | 12 | 41 |
| 7 | Reading | 25 | 12 | 5 | 8 | 40 | 36 | 4 | 41 |
| 8 | Leyton Orient | 25 | 11 | 5 | 9 | 32 | 22 | 10 | 38 |
| 9 | Bolton WanderersBolton | 25 | 11 | 5 | 9 | 38 | 39 | -1 | 38 |
| 10 | Mansfield TownMansfield | 24 | 11 | 4 | 9 | 32 | 28 | 4 | 37 |
| 11 | Lincoln CityLincoln | 26 | 9 | 8 | 9 | 29 | 30 | -1 | 35 |
| 12 | Charlton AthleticCharlton | 24 | 9 | 7 | 8 | 29 | 25 | 4 | 34 |
| 13 | Rotherham UnitedRotherham | 25 | 9 | 7 | 9 | 28 | 26 | 2 | 34 |
| 14 | Blackpool | 25 | 7 | 10 | 8 | 34 | 37 | -3 | 31 |
| 15 | Stevenage | 24 | 8 | 7 | 9 | 19 | 22 | -3 | 31 |
| 16 | Exeter CityExeter | 25 | 9 | 4 | 12 | 28 | 32 | -4 | 31 |
| 17 | Wigan AthleticWigan | 24 | 8 | 6 | 10 | 23 | 24 | -1 | 30 |
| 18 | Bristol Rovers | 25 | 8 | 4 | 13 | 25 | 39 | -14 | 28 |
| 19 | Peterborough UnitedPeterborough | 25 | 7 | 5 | 13 | 41 | 46 | -5 | 26 |
| 20 | Northampton TownNorthampton | 26 | 6 | 8 | 12 | 24 | 40 | -16 | 26 |
| 21 | Crawley TownCrawley | 24 | 5 | 6 | 13 | 25 | 44 | -19 | 21 |
| 22 | Shrewsbury TownShrewsbury | 25 | 5 | 5 | 15 | 26 | 45 | -19 | 20 |
| 23 | Cambridge UnitedCambridge | 25 | 4 | 6 | 15 | 24 | 45 | -21 | 18 |
| 24 | Burton Albion | 25 | 2 | 9 | 14 | 21 | 39 | -18 | 15 |
| > League One Full Table | |||||||||
