After three draws against the same opponents at home in last month's Test series, New Zealand will head to England to contest two Tests, three one-day internationals, two Twenty20 games and the ICC Champions Trophy.
The tour begins with a three-day match against Derbyshire, starting on May 4.
Other than the additions of Gillespie and Guptill, New Zealand's Test squad shows no changes from the group that could not force a positive result in the home series against England.
Former captain Daniel Vettori is named in the limited-overs squad for the tour but not in the Test ranks, after recovering from an ankle injury that has kept him sidelined from Black Caps duty for eight months.
The limited-overs touring party also includes the Wellington wicketkeeper Luke Ronchi, who has previously played seven internationals for Australia.
New Zealand national selection manager Kim Littlejohn said: "The ODI squad has a core group of players who have now played in a number of international tournaments and bring a wealth of experience. Having Daniel Vettori back in the side adds to that and we're really excited to have someone of his quality back in the team.
"Luke Ronchi gets his chance after impressing on the domestic scene. We know how dangerous he is and look forward to seeing him display his talents on the international stage."
Test squad: Brendon McCullum (captain), Trent Boult, Doug Bracewell, Dean Brownlie, Peter Fulton, Martin Guptill, Mark Gillespie, Tom Latham, Bruce Martin, Hamish Rutherford, Tim Southee, Ross Taylor, Neil Wagner, Bradley John Watling, Kane Williamson.
ODI, Twenty20 and ICC Champions Trophy squad: Brendon McCullum (captain), Trent Boult, Grant Elliott, Andrew Ellis, James Franklin, Martin Guptill, Mitchell McClenaghan, Nathan McCullum, Kyle Mills, Colin Munro, Luke Ronchi, Tim Southee, Ross Taylor, Daniel Vettori, Kane Williamson.