Jamieson reached Bengaluru late on Thursday night and was expected to train with the team on Friday.
The 28-year-old giant, who had back surgery in February, was earlier with the team in India as cover for Tim Southee.
Jamieson has taken 14 wickets in 13 ODIs and so far has had more success in Test cricket.
But his height and ability to move the ball could cause problems in India, with Stead saying: “We are fortunate to have a player of Kyle’s caliber waiting in the wings.
“His skill and physical attributes always make him a threat with the ball and it is an added bonus that he was able to train with us over the first two weeks of the tournament.”
New Zealand are struggling with injuries and both star batsman Kane Williamson (thumb) and all-rounder Mark Chapman (thigh) are currently out.
They will be in Bengaluru for their final group match against Sri Lanka on Thursday.