The wall was principally constructed by legionaries from the three British legions, II Augusta (based at Caerleon in South Wales), XX Valeria Victrix (based at Chester), and VI Victrix (based at York but which appears to have arrived with Hadrian in AD 122). The troops from these legions left building inscriptions recording their work at various points, ranging from the monumental at milecastles and forts, down to informal on the curtain wall itself, commemorating individual stints by centuries of legionaries. A detachment of the British fleet was involved in the construction of the fort at Benwell.
We know from similar inscriptions that other troops (including auxiliaries and detachments from the fleet) and even civilians were involved in building or repair work at various times during the life of the Wall.
Further reading: Breeze and Dobson 2000