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