Former captain Vettori hasn't played a Test for nearly a year, mainly because of Achilles trouble, and was only originally selected for the one-day leg of this tour.
But a calf injury suffered by his fellow left-arm spinner Bruce Martin during New Zealand's thumping 170-run first Test defeat at Lord's saw Vettori make an earlier than expected arrival in England.
The 34-year-old, who bowled in the Headingley nets on Wednesday, is vying for a place with seamer Doug Bracewell, not selected at Lord's.
If Vettori is included, he will become New Zealand's single most-capped Test player, topping the mark of 111 appearances he shares with Stephen Fleming.
Also Read
Vettori's record shows 112 Tests but one of those was for an ICC World XI against Australia in 2005.
"It's exciting seeing Dan around the changing room and training with us again," Black Caps left-arm seamer Neil Wagner said Wednesday.
New Zealand have confirmed captain Brendon McCullum will keep wicket at Headingley after BJ Watling was ruled out with a knee injury suffered during the first Test.
McCullum, who deputised for Watling at Lord's, gave up keeping in Tests because of a back complaint in 2010.
Watling's absence has seen New Zealand announce they will play an extra batsman at Headingley in Martin Guptill, who has experience of English conditions from his time with Derbyshire.