The teenager will make his Test debut for New Zealand in the final and third Test against England at the Mclean Park.
Southee, who turned 19 in Dec, was named in the side on Friday to replace the injured Kyle Mills.
"It's pretty exciting for him," the 29-year-old Vettori told reporters on Friday. "He is pretty calm about it all. "I have talked to him and said I just wanted him to play his natural game."
Southee, who played in the Twenty20 matches against England at the start of the tour. The swing bowler took 17 wickets at an average of 6.64.
"The way he has bowled in the past has led us to believe he can do a job for us," Vettori added.
"He is pretty consistent. He swings it and with those two things it doesn't matter what kind of wicket it is you bowl on.
"He is an exciting prospect for us and we are looking forward to him beginning a long career for us." Vettori, who was just 18 when he made his test debut against England in 1997, said he did not expect Southee's age to play any part in the game.
"It comes down to the person," he said. "The age is irrelevant.
"Tim has two full seasons of first class cricket and played pretty well. He has gone away to the under-19 tournament and probably dominated the tournament. "He did a good job in the Twenty20s and is in good form. I don't' see why it'll be a problem.
"He's got a good head on him. He's calm and mature and you'll see that when he plays you'll see he is a guy who has going to be a huge asset for New Zealand cricket for some time to come."