In short
The twelve disciples became apostles when they were given authority to do the miracles listed in Matthew 10:1, and were equipped for this office by hearing his teaching and seeing his miracles.
The fact that the twelve disciples are given authority to conduct the miracles listed in Matthew 10:1 indicates that they are now officially confirmed in the special office of apostle. In typical businesslike fashion, the evangelist Matthew lists these gifts only very briefly. These men have been equipped for the office of apostle because they have sat under Jesus’ preaching for some time and they have witnessed his miracles firsthand.1
1 And he called to him his twelve disciples and gave them authority over unclean spirits, to cast them out, and to heal every disease and every affliction.