But there was no room in the 17-man squad for all-rounders James Faulkner and Glenn Maxwell, who were part of Australia's one-day World Cup winning side.
Joe Burns was also overlooked, despite scoring two half-centuries in Australia's last Test, against India in January.
Paceman James Pattinson missed out with a hamstring injury, opening the door once again for Peter Siddle.
Australia play two Tests in the West Indies from June 5, with their five-Test Ashes series starting in England on July 8.
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Voges won his place on the plane for similar reasons, with the 35-year-old Western Australian captain smashing 1,358 Shield runs to be the season's highest scorer and player of the year with an average of 104.46.
New South Wales keeper Nevill was picked as Brad Haddin's understudy, preferred to Matthew Wade.
National selector Rod Marsh said the Test team had performed very well in recent times, and the big challenge was to maintain the form away from home.