Captain Michael Clarke was also among the 14 players selected for the seven-game series in India from October 11, which will be coached by Steve Rixon while Darren Lehmann is rested.
Whether Clarke makes the trip or not depends on treatment for his chronic back problem, with national selector John Inverarity making clear he was picked “subject to fitness.”
Haddin was the surprise inclusion, winning his place on the back of a lean England one-day series by alternative keeper Matthew Wade, which Australia won 2-1.
Haddin, 35, was drafted back into the Test side in place of Wade for the recent Ashes series against England to serve as Clarke's vice-captain. He broke Rod Marsh's 30-year-old record for the most dismissals in an Ashes series, but was not in the team for the subsequent one-day matches.
“Matthew Wade has been omitted due to lack of form and has been replaced by Brad Haddin, who captured an Ashes series record of dismissals in July and August,” said Inverarity.
“Matthew is 25 years of age and has a great deal of natural ability both as a batsman and as a keeper. The selectors are confident that Matthew will regain form and press hard for selection in the not-too-distant future.”
The glaring ommission for India was the dynamic Warner, who missed the first two Ashes Tests after being suspended in the run-up to the series for punching England's Joe Root in a Birmingham bar following Australia's Champions Trophy defeat to their arch-rivals.
He was then dropped for the one-day matches against England and returned home early to Australia.
Inverarity made no comment on the left-hander but Clarke earlier in the day backed him to bounce back from his England disappointment, saying he remained a vital part of the Australian set-up despite his problems.
“Davey is certainly a big part of the Australian team, whatever format,”said Clarke.
“He knows we've got a huge summer ahead and when an opportunity comes up again, I'm sure he'll grab it with both hands.”
Pakistan-born Ahmed, who made his international debut in England, also missed out. Xavier Doherty replaces him as the only specialist spinner in the squad.
Inverarity said Ahmed bowled well in England with limited opportunities, but Doherty was better suited to Indian conditions.
Whether Clarke is on the plane depends on the progress of treatment for his back, which has plagued him for years.
The captain returned to Sydney late Wednesday and said he would consult team physiotherapist Alex Kountouris and probably undergo scans.
“No doubt it's quite stiff and sore,” he said of his back.
“But I'll be guided by the experts on what I need to do now to try and get myself as fit as I can be. I would certainly like to go and continue to play.”
Rixon will coach the tour with Lehmann, who took over from the sacked Mickey Arthur just before the Ashes started, given time to rest ahead of the return series against England starting in November.
“Darren has been on the road and away from home for a considerable amount of time. This is a great opportunity for Darren to refresh, work with the states and provide others with opportunities,” said Inverarity.
Australia: Michael Clarke (capt), George Bailey (vice-capt), Nathan Coulter-Nile, Xavier Doherty, James Faulkner, Aaron Finch, Brad Haddin, Moises Henriques, Phil Hughes, Mitchell Johnson, Glenn Maxwell, Clint McKay, Adam Voges, Shane Watson
