Watson continues in the all-rounder role as left-hander Chris Rogers, 35 - who played one Test in 2008 - returns for the series which starts on 10 July.
Left-armer James Faulkner is the sole uncapped player but only five of the 16 have played an Ashes Test in England.
Australia Ashes Tour itinerary
1st Test, Trent Bridge
2nd Test, Lord's
3rd Test, Old Trafford
4th Test, Durham
5th Test, The Oval
His inclusion means there is no place for left-arm seamer Mitchell Johnson, who has taken 35 wickets in nine Tests against England. He is one of five players omitted from the squad which went to India.
The veteran gloveman, who averages 35 with the bat in his 44 Tests, returned to the team for the third Test in India after Wade was injured, but lost his place again for the final match of the series.
There is also room in the squad for 25-year-old Wade. In 12 Tests, he has averaged 34 with the bat, including two centuries.
Commenting on Haddin's return, selector John Inverarity said: "We feel it's important to have a senior, seasoned player support Michael [Clarke] at this time.
"When Shane Watson advised of his decision to stand down, the NSP (national selection panel) viewed Brad as the exceptional candidate to step into this leadership void."
Rogers, who scored only four and 15 in his solitary Test to date against India in Perth, has considerable experience of English conditions. He is the current captain of Middlesex, having also played for Derbyshire, Leicestershire and Northants.
He has made 19,107 runs in 233 first-class matches at an average of 50.01.
Faulkner, who turns 23 next Monday, has impressed with 125 wickets at 22.34 in 34 first-class matches for Tasmania.
He has also captured eight wickets at 26.37 in five one-day internationals and four wickets at 17.50 in three Twenty20 matches for Australia.
Fawad Ahmed, the Pakistan-born leg-spinner who is seeking asylum but has not yet received his Australian passport, has not been included, leaving Nathan Lyon as the only spinner in the 16.
Ashes Tests in England
Lyon was Australia's most successful bowler in India with 15 wickets, including 7-94 in the final match in Delhi. He has taken 76 wickets in his 22 Tests at an average of 33.
Having lost the first two Tests in India, Australia coach Mickey Arthur asked each member of his squad to produce, by email or in person, three ideas about how the team could improve but Watson, Johnson, Usman Khawaja and James Pattinson failed to respond and were dropped for the third Test.
Watson, 31, returned home to consider his international future but flew back to India, where he
captained the side
in the final match in the absence of the injured Clarke.
"The tour to India was very demanding and a learning experience for all," added Inverarity.
"The result was unacceptable and the players, coaches, support staff and NSP are smarting from those performances and are galvanised to ensure that we play tough, competitive cricket throughout the Ashes."
Regular skipper Clarke is expected to be fit for the Ashes despite the news last month that he would be out for up to 10 weeks with a
recurrence of a back problem.
Australia, who have lost the last two Ashes series, are fourth in the Test rankings.
Haddin will captain the Australia A side which will tour the British Isles ahead of the Ashes and play against Scotland, Ireland and Gloucestershire.
That squad contains a number of players also selected for the Ashes.
Australia Ashes squad:
Michael Clarke (captain), Brad Haddin (vice-captain), Jackson Bird, Ed Cowan, James Faulkner, Ryan Harris, Phil Hughes, Usman Khawaja, Nathan Lyon, James Pattinson, Chris Rogers, Peter Siddle, Mitchell Starc, Matthew Wade, David Warner, Shane Watson.
Australia A squad to tour the British Isles:
Brad Haddin (captain), Steve Smith (vice-captain), Ashton Agar, Jackson Bird, Alex Doolan, Ryan Harris, Moises Henriques, Usman Khawaja, Nathan Lyon, Nic Maddinson, James Pattinson, Chadd Sayers, Peter Siddle, Jordan Silk.
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