Bond, who has 43 wickets from 10 Tests, only recently resumed playing in domestic cricket after suffering recurrence of a lower back stress fracture in May.
Astle also returned to the trail after injuring both his knees over last year.
He has not taken part in a One-day International since the World Cup in South Africa and played his last Test in India in November.
New Zealand open their series on May 20 at Lords, followed by Tests at Headingly starting on June 3 and Trent Bridge on June 10.
The bulk of the team is expected to remain in England for the tri-series including the West Indies, with specialist One-day players to be added.
Squad: Michael Papps, Mark Richardson, Stephen Fleming (captain), Scott Styris, Craig McMillan, Nathan Astle, Chris Cairns, Jacob Oram, Brendon McCullum, Daniel Vettori, Daryl Tuffey, Chris Martin, Kyle Mills, Shane Bond.