Bond had been suffering from stress fractures of the lower back while Tuffey and Astle have recovered from knee injury.
"All three guys have worked extremely hard to get themselves ready for this tour," New Zealand coach John Bracewell told reporters after the trio had undergone rigorous testing at the Lincoln Centre of Excellence near Christchurch.
"Each player went through their own 'injury specific' testing process."
He added Tuffey had reported no significant pain in his knee after bowling for long spells followed by a rest, just as he would do in a Test match.
Bond was first injured during the tour of Sri Lanka last May and returned home to recuperate.
He went back to playing club cricket in Christchurch in November but then broke down again within a month and missed the home series against Pakistan and South Africa.
INCREASING INTENSITY
Since then, he has been gradually increasing the intensity of his programme, Bracewell said.
"He has also been ensuring he maintains the technical adjustments to his action which he has made," he added.
Astle toured India but returned home in October after the Test matches, missing the triangular one-day series which also involved Australia.
He underwent keyhole surgery on his troublesome right knee and missed the recent South Africa series.
"Nathan Astle was put through game situation testing and his knee responded well," Bracewell said. "Now it's just a case of continuing to increase his confidence and that will grow with each practice or match."
The 14-man New Zealand squad leaves for England on Tuesday. Their three-test tour series begins at Lord's on May 20.
New Zealand all rounder Chris Cairns has said he will end his Test career at Trent Bridge, where the third and final Test starts on June 10. Cairns played for Nottinghamshire from 1989 to 1996 and again in 2003.
Squad: Stephen Fleming (captain), Nathan Astle, Shane Bond, Chris Cairns, Chris Martin, Kyle Mills, Brendon McCullum, Craig McMillan, Jacob Oram, Michael Papps, Mark Richardson, Scott Styris, Daryl Tuffey, Daniel Vettori.
