The team announced both two-way contracts on Monday.
Veilleux returned to the Wild in a trade deadline deal with New Jersey in February. The hard-nosed veteran played his first six seasons with the Wild and gave the team a boost in energy upon his return to Minnesota.
Rau scored two goals in nine games with the Wild last season. The Eden Prairie native had a solid season in the minors with Houston of the AHL, scoring 14 goals with 21 assists in 67 games.