Williamson, the third ranked Test batsman in the world, missed the recent Twenty20 series with the problem but is fit to lead a 15-man squad in the two-Test series.
The 29-year-old will captain his side in the first Test at his home ground in Mount Maunganui, starting on November 21, and selector Gavin Larsen is delighted to have him available.
“Kane’s made good progress over the past fortnight and we’re delighted to welcome back a player of his class and experience,” Larsen said in a statement.
“It’s obviously going to be a very special Test for him and Trent Boult, being such passionate locals – we know there’s already a lot of excitement in that part of the Bay of Plenty.”
Bairstow and Mike Cowan were named vice-presidents.
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