Vunipola, who was excellent for Saracens in Saturday's Premiership final, suffered a concussion in the game but was included in the squad having last played in the 2021 Six Nations.
Halfback Care's last cap came against Japan in 2018, though the 35-year-old, who has had a superb season for Harlequins, did come off the bench in England's non-cap 52-21 defeat by the Barbarians on Sunday
There are eight uncapped players in the squad - Fraser Dingwall, Tommy Freeman, Guy Porter, Patrick Schickerling, Jack van Poortvliet and Jack Walker, along with Henry Arundell and Will Joseph who are named as apprentice players.
Alex Dombrandt, Joe Cokanasiga, George Ford, Sam Simmonds, Henry Slade, Manu Tuilagi, Kyle Sinckler, Anthony Watson, Louis Lynagh and George Furbank were unavailable through injury, while Ben Youngs also misses the trip due to family reasons.
Prop Joe Marler was another big name not to make the trip, along with Premiership player of the year Ben Earl.
"Though we have 10 players unavailable due to injury, we have picked a very strong squad capable of winning the series," Jones said.
"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."
The first Test is in Perth on July 2 followed by Brisbane and Sydney in the following two weeks.Â
England have won their past eight games against Australia, all under Jones, starting with a clean sweep of their three-Test tour in 2016.
ENGLAND SQUAD
Forwards: Ollie Chessum (Leicester Tigers, 2 caps) Luke Cowan-Dickie (Exeter Chiefs, 34 caps) Tom Curry (Sale Sharks, 40 caps) Charlie Ewels (Bath Rugby, 30 caps) Ellis Genge (Leicester Tigers, 36 caps) Jamie George (Saracens, 66 caps) Joe Heyes (Leicester Tigers, 2 caps) Jonny Hill (Exeter Chiefs, 12 caps) Nick Isiekwe (Saracens, 7 caps) Maro Itoje (Saracens, 56 caps) Courtney Lawes (Northampton Saints, 93 caps) Lewis Ludlam (Northampton Saints, 11 caps) Bevan Rodd (Sale Sharks, 2 caps) Patrick Schickerling (Exeter Chiefs, uncapped) Will Stuart (Bath Rugby, 20 caps) Sam Underhill (Bath Rugby, 28 caps) Billy Vunipola (Saracens, 61 caps) Mako Vunipola (Saracens, 67 caps) Jack Walker (Harlequins, uncapped) Jack Willis (Wasps, 3 caps)
Backs: Henry Arundell (London Irish, uncapped) *apprentice player Danny Care (Harlequins, 84 caps) Joe Cokanasiga (Bath Rugby, 11 caps) Fraser Dingwall (Northampton Saints, uncapped) Owen Farrell (Saracens, 94 caps) Tommy Freeman (Northampton Saints, uncapped) George Furbank (Northampton Saints, 6 caps) Will Joseph (London Irish, uncapped) *apprentice player Joe Marchant (Harlequins, 12 caps) Jonny May (Gloucester Rugby, 69 caps) Jack Nowell (Exeter Chiefs, 39 caps) Guy Porter (Leicester Tigers, uncapped) Harry Randall (Bristol Bears, 6 caps) Jack van Poortvliet (Leicester Tigers, uncapped) Marcus Smith (Harlequins, 10 caps) Freddie Steward (Leicester Tigers, 10 caps) (Reporting by Mitch Phillips, editing by)
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