The ALPHA experiment at the CERN Antiproton Decelerator facility underwent a major upgrade in 2018. Amongst other improvements, key is the rotation of the atom magnetic trap axis, which is now vertical. Bilfinger Noell designed and fabricated the 2 m long superconducting vertical solenoid, which provides the 1 T background field for the experiment. This is an active shielded, conduction cooled, NbTi magnet with a warm bore of 0.5 m diameter. The system is designed to achieve a field precision of less than 10 ppm in the control volume and a charging time of less than 20 minutes. This contribution describes the main design features of the system and the results of the cold tests.