Stokes was named in the 16-man squad, and retains the vice-captaincy, despite being arrested in Bristol Monday and spending a night in prison after an altercation with a member of the public.
Surrey wicketkeeper Ben Foakes, leg-spinner Mason Crane and Somerset seamer Craig Overton are the players going on tour who have no experience at Test match level.
Vince averages just 19 from seven Tests and was dropped last year while Ballance struggled for runs in the home series against South Africa this summer before he fractured his finger and was ruled out.
Dawid Malan and opener Mark Stoneman hold onto their places despite not setting the world alight in the most recent series against the West Indies while Tom Westley has been dropped.
Seamer Toby Roland-Jones has been ruled out with injury which means a recall for Nottinghamshire seamer Jake Ball.
England selector James Whittaker said: “A tour of Australia is the ultimate test for our squad. We have provided Joe Root and Trevor Bayliss with a well-balanced squad with options in all areas.
“After a successful summer, having won the Test series against South Africa and West Indies, there is real competition for places and we have selected a squad that will work hard and compete against Australia, aiming to win the Ashes.
“Surrey’s Ben Foakes deserves his selection for the first time at this level. His glovework has been exemplary and he is regarded as a wicketkeeper of the highest quality.
“He has the ability to contribute with the bat scoring over 680 runs in the Championship this summer at an average of 45.33.