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 | 20 | 15 | 3 | 2 | 37 | 16 | 21 | 48 |
| 2 | Wycombe WanderersWycombe | 21 | 14 | 5 | 2 | 46 | 22 | 24 | 47 |
| 3 | Wrexham | 22 | 13 | 6 | 3 | 33 | 15 | 18 | 45 |
| 4 | Huddersfield TownHuddersfield | 21 | 13 | 3 | 5 | 35 | 18 | 17 | 42 |
| 5 | Stockport CountyStockport | 22 | 10 | 6 | 6 | 34 | 23 | 11 | 36 |
| 6 | Reading | 21 | 10 | 4 | 7 | 34 | 31 | 3 | 34 |
| 7 | Barnsley | 22 | 9 | 6 | 7 | 31 | 31 | 0 | 33 |
| 8 | Mansfield TownMansfield | 20 | 9 | 4 | 7 | 26 | 22 | 4 | 31 |
| 9 | Lincoln CityLincoln | 22 | 8 | 7 | 7 | 28 | 26 | 2 | 31 |
| 10 | Bolton WanderersBolton | 20 | 9 | 4 | 7 | 29 | 31 | -2 | 31 |
| 11 | Charlton AthleticCharlton | 21 | 8 | 6 | 7 | 25 | 20 | 5 | 30 |
| 12 | Exeter CityExeter | 21 | 9 | 3 | 9 | 22 | 23 | -1 | 30 |
| 13 | Leyton Orient | 21 | 8 | 4 | 9 | 26 | 20 | 6 | 28 |
| 14 | Wigan AthleticWigan | 21 | 7 | 6 | 8 | 20 | 18 | 2 | 27 |
| 15 | Blackpool | 21 | 7 | 6 | 8 | 30 | 33 | -3 | 27 |
| 16 | Stevenage | 20 | 7 | 5 | 8 | 15 | 20 | -5 | 26 |
| 17 | Peterborough UnitedPeterborough | 21 | 7 | 3 | 11 | 38 | 40 | -2 | 24 |
| 18 | Rotherham UnitedRotherham | 20 | 6 | 5 | 9 | 19 | 22 | -3 | 23 |
| 19 | Bristol Rovers | 21 | 6 | 4 | 11 | 19 | 32 | -13 | 22 |
| 20 | Northampton TownNorthampton | 22 | 5 | 6 | 11 | 22 | 38 | -16 | 21 |
| 21 | Crawley TownCrawley | 21 | 5 | 4 | 12 | 20 | 36 | -16 | 19 |
| 22 | Cambridge UnitedCambridge | 21 | 4 | 5 | 12 | 21 | 37 | -16 | 17 |
| 23 | Shrewsbury TownShrewsbury | 21 | 4 | 3 | 14 | 22 | 41 | -19 | 15 |
| 24 | Burton Albion | 21 | 2 | 6 | 13 | 17 | 34 | -17 | 12 |
| > League One Full Table | |||||||||
