Harlequins number eight Alex Dombrandt is injured so Vunipola, who last played in the 2021 Six Nations, returns.
Scrum-half Care is named but England's most capped male player, Ben Youngs, does not travel with the squad.
The first Test is in Perth on 2 July, followed by matches in Brisbane on 9 July and Sydney on 16 July.
Care, 35, won the last of his 84 caps in 2018, but played for England in the 52-21 non-cap loss to 14-man Barbarians at Twickenham on Sunday.
Head coach Eddie Jones said: "Though we have ten players unavailable due to injury, we have picked a very strong squad capable of winning the series.
"This squad is a real mix of young, talented players and some very experienced, senior players and we're looking forward to bring the group together.
"This tour will be a great experience for the group and a crucial part of the team's work towards the Rugby World Cup in 2023. We will continue to develop the base of the squad and how we want to play.
"We've put a lot of work into preparation for the tour over the past few weeks but now the hard work really begins when we finally get the squad on the plane and to Australia."
Forwards: Ollie Chessum (Leicester Tigers), Luke Cowan-Dickie (Exeter Chiefs), Tom Curry (Sale Sharks), Charlie Ewels (Bath Rugby), Ellis Genge (Leicester Tigers), Jamie George (Saracens), Joe Heyes (Leicester Tigers), Jonny Hill (Exeter Chiefs), Nick Isiekwe (Saracens), Maro Itoje (Saracens), Courtney Lawes (Northampton Saints), Lewis Ludlam (Northampton Saints), Bevan Rodd (Sale Sharks), Patrick Schickerling (Exeter Chiefs), Will Stuart (Bath Rugby), Sam Underhill (Bath Rugby), Billy Vunipola (Saracens), Mako Vunipola (Saracens), Jack Walker (Harlequins), Jack Willis (Wasps).
Backs: Henry Arundell (London Irish), Danny Care (Harlequins), Joe Cokanasiga (Bath Rugby), Fraser Dingwall (Northampton Saints), Owen Farrell (Saracens), Tommy Freeman (Northampton Saints), George Furbank (Northampton Saints), Will Joseph (London Irish), Joe Marchant (Harlequins), Jonny May (Gloucester Rugby), Jack Nowell (Exeter Chiefs), Guy Porter (Leicester Tigers), Harry Randall (Bristol Bears), Jack van Poortvliet (Leicester Tigers), Marcus Smith (Harlequins), Freddie Steward (Leicester Tigers).