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 | 23 | 16 | 5 | 2 | 41 | 17 | 24 | 53 |
| 2 | Wycombe WanderersWycombe | 24 | 15 | 6 | 3 | 50 | 26 | 24 | 51 |
| 3 | Wrexham | 25 | 15 | 6 | 4 | 37 | 18 | 19 | 51 |
| 4 | Huddersfield TownHuddersfield | 23 | 13 | 5 | 5 | 36 | 19 | 17 | 44 |
| 5 | Barnsley | 25 | 12 | 6 | 7 | 39 | 33 | 6 | 42 |
| 6 | Reading | 24 | 12 | 5 | 7 | 39 | 33 | 6 | 41 |
| 7 | Stockport CountyStockport | 25 | 10 | 8 | 7 | 37 | 27 | 10 | 38 |
| 8 | Leyton Orient | 24 | 11 | 4 | 9 | 32 | 22 | 10 | 37 |
| 9 | Mansfield TownMansfield | 23 | 11 | 4 | 8 | 31 | 26 | 5 | 37 |
| 10 | Bolton WanderersBolton | 23 | 11 | 4 | 8 | 35 | 34 | 1 | 37 |
| 11 | Charlton AthleticCharlton | 23 | 9 | 7 | 7 | 27 | 21 | 6 | 34 |
| 12 | Lincoln CityLincoln | 25 | 8 | 8 | 9 | 28 | 30 | -2 | 32 |
| 13 | Stevenage | 23 | 8 | 7 | 8 | 18 | 20 | -2 | 31 |
| 14 | Exeter CityExeter | 24 | 9 | 4 | 11 | 28 | 31 | -3 | 31 |
| 15 | Blackpool | 24 | 7 | 9 | 8 | 32 | 35 | -3 | 30 |
| 16 | Rotherham UnitedRotherham | 23 | 7 | 7 | 9 | 21 | 23 | -2 | 28 |
| 17 | Wigan AthleticWigan | 23 | 7 | 6 | 10 | 21 | 23 | -2 | 27 |
| 18 | Northampton TownNorthampton | 25 | 6 | 8 | 11 | 24 | 39 | -15 | 26 |
| 19 | Peterborough UnitedPeterborough | 24 | 7 | 4 | 13 | 41 | 46 | -5 | 25 |
| 20 | Bristol Rovers | 24 | 7 | 4 | 13 | 22 | 38 | -16 | 25 |
| 21 | Crawley TownCrawley | 23 | 5 | 5 | 13 | 24 | 43 | -19 | 20 |
| 22 | Shrewsbury TownShrewsbury | 24 | 4 | 5 | 15 | 24 | 44 | -20 | 17 |
| 23 | Cambridge UnitedCambridge | 24 | 4 | 5 | 15 | 22 | 43 | -21 | 17 |
| 24 | Burton Albion | 24 | 2 | 8 | 14 | 20 | 38 | -18 | 14 |
| > League One Full Table | |||||||||
